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numericals.bib
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% Encoding: UTF-8
@InProceedings{Bras-Amoros2018inproc-Different,
author = {Maria Bras{-}Amor{\'{o}}s},
title = {Different tree approaches to the problem of counting numerical semigroups by genus},
booktitle = {Proceedings of the 11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, GASCom 2018, Athens, Greece, June 18-20, 2018.},
year = {2018},
pages = {7--11},
bibsource = {dblp computer science bibliography, https://dblp.org},
biburl = {https://dblp.org/rec/bib/conf/gascom/Bras-Amoros18},
crossref = {DBLP:conf/gascom/2018},
file = {:numericals/Bras-Amoros2018inproc-Different.pdf:PDF},
timestamp = {Sun, 22 Jul 2018 18:56:12 +0200},
url = {http://ceur-ws.org/Vol-2113/invited2.pdf},
}
@Article{Bras-Amoros2008SF-Fibonacci,
author = {Bras-Amor\'{o}s, Maria},
title = {Fibonacci-like behavior of the number of numerical semigroups of a given genus},
journal = {Semigroup Forum},
year = {2008},
volume = {76},
number = {2},
pages = {379--384},
issn = {0037-1912},
doi = {10.1007/s00233-007-9014-8},
file = {:numericals/Bras-Amoros2008SF-Fibonacci.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {2377597},
mrreviewer = {J. L. Chrislock},
url = {https://doi.org/10.1007/s00233-007-9014-8},
}
@Article{Bras-AmorosBulygin2009SF-Towards,
author = {Bras-Amor{\'o}s, Maria and Bulygin, Stanislav},
title = {Towards a better understanding of the semigroup tree},
journal = {Semigroup Forum},
year = {2009},
volume = {79},
number = {3},
pages = {561--574},
issn = {0037-1912},
coden = {SMGFAN},
doi = {10.1007/s00233-009-9175-8},
file = {:numericals/Bras-AmorosBulygin2009SF-Towards.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {MR2564064},
url = {http://dx.doi.org/10.1007/s00233-009-9175-8},
}
@Article{Bras-Amoros2009JPAA-Bounds,
author = {Bras-Amor\'os, Maria},
title = {Bounds on the number of numerical semigroups of a given genus},
journal = {J. Pure Appl. Algebra},
year = {2009},
volume = {213},
number = {6},
pages = {997--1001},
issn = {0022-4049},
doi = {10.1016/j.jpaa.2008.11.012},
file = {:numericals/Bras-Amoros2009JPAA-Bounds.pdf:PDF},
fjournal = {Journal of Pure and Applied Algebra},
mrclass = {05A15 (05A16 20M14)},
mrnumber = {2498791},
url = {http://dx.doi.org/10.1016/j.jpaa.2008.11.012},
}
@Article{DelgadoGarci2016ACCA-numericalsgps,
author = {Delgado, M. and García-Sánchez, P. A.},
title = {{$numericalsgps$}, a {$GAP$} package for numerical semigroups},
journal = {ACM Commun. Comput. Algebra},
year = {2016},
volume = {50},
number = {1},
pages = {12--24},
issn = {1932-2232},
doi = {10.1145/2930964.2930966},
file = {:numericals/DelgadoGarci2016ACCA-numericalsgps.pdf:PDF},
fjournal = {ACM Communications in Computer Algebra},
mrclass = {20-04 (20M14 68W30)},
mrnumber = {3493240},
url = {http://dx.doi.org/10.1145/2930964.2930966},
}
@Article{DelgadoGarciRobles-Perez2016LJCM-Numerical,
author = {Delgado, M. and García-Sánchez, P. A. and Robles-Pérez, A. M.},
title = {Numerical semigroups with a given set of pseudo-{F}robenius numbers},
journal = {LMS J. Comput. Math.},
year = {2016},
volume = {19},
number = {1},
pages = {186--205},
issn = {1461-1570},
doi = {10.1112/S1461157016000061},
file = {:numericals/DelgadoGarciRobles-Perez2016LJCM-Numerical.pdf:PDF},
fjournal = {LMS Journal of Computation and Mathematics},
mrclass = {20M14 (11D07)},
mrnumber = {3490354},
url = {http://dx.doi.org/10.1112/S1461157016000061},
}
@Article{Elizalde2010JPAA-Improved,
author = {Elizalde, Sergi},
title = {Improved bounds on the number of numerical semigroups of a given genus},
journal = {J. Pure Appl. Algebra},
year = {2010},
volume = {214},
number = {10},
pages = {1862--1873},
issn = {0022-4049},
coden = {JPAAA2},
doi = {10.1016/j.jpaa.2009.12.031},
file = {:numericals/Elizalde2010JPAA-Improved.pdf:PDF},
fjournal = {Journal of Pure and Applied Algebra},
mrclass = {20M14 (05A15)},
mrnumber = {2608114 (2011i:20088)},
url = {http://dx.doi.org/10.1016/j.jpaa.2009.12.031},
}
@Article{FromentinHivert2016MC-Exploring,
author = {Fromentin, Jean and Hivert, Florent},
title = {Exploring the tree of numerical semigroups},
journal = {Math. Comp.},
year = {2016},
volume = {85},
number = {301},
pages = {2553--2568},
issn = {0025-5718},
doi = {10.1090/mcom/3075},
file = {:numericals/FromentinHivert2016MC-Exploring.pdf:PDF},
fjournal = {Mathematics of Computation},
mrclass = {68R05 (05A15 68W10)},
mrnumber = {3511292},
mrreviewer = {Manuel Augusto Fernandes Delgado},
url = {http://dx.doi.org/10.1090/mcom/3075},
}
@Article{Kaplan2012JPAA-Counting,
author = {Kaplan, Nathan},
title = {Counting numerical semigroups by genus and some cases of a question of {W}ilf},
journal = {J. Pure Appl. Algebra},
year = {2012},
volume = {216},
number = {5},
pages = {1016--1032},
issn = {0022-4049},
doi = {10.1016/j.jpaa.2011.10.038},
file = {:numericals/Kaplan2012JPAA-Counting.pdf:PDF},
fjournal = {Journal of Pure and Applied Algebra},
mrclass = {20M14 (05A15)},
mrnumber = {2875324},
mrreviewer = {Vadim Ponomarenko},
url = {http://dx.doi.org/10.1016/j.jpaa.2011.10.038},
}
@Article{Wilf1978AMM-circle,
author = {Wilf, Herbert S.},
title = {A circle-of-lights algorithm for the ``money-changing problem''},
journal = {Amer. Math. Monthly},
year = {1978},
volume = {85},
number = {7},
pages = {562--565},
issn = {0002-9890},
doi = {10.2307/2320864},
file = {:numericals/Wilf1978AMM-circle.pdf:PDF},
fjournal = {The American Mathematical Monthly},
mrclass = {10A30 (05A17 68A10)},
mrnumber = {0556658},
mrreviewer = {Dennis White},
url = {http://dx.doi.org/10.2307/2320864},
}
@Article{Zhai2012SF-Fibonacci,
author = {Zhai, Alex},
title = {Fibonacci-like growth of numerical semigroups of a given genus},
journal = {Semigroup Forum},
year = {2013},
volume = {86},
number = {3},
pages = {634-662},
issn = {0037-1912},
doi = {10.1007/s00233-012-9456-5},
file = {:numericals/Zhai2012SF-Fibonacci.pdf:PDF},
keywords = {Numerical semigroup; Genus of numerical semigroup},
publisher = {Springer-Verlag},
url = {https://dx.doi.org/10.1007/s00233-012-9456-5},
}
@Article{Zhao2010SF-Constructing,
author = {Zhao, Yufei},
title = {Constructing numerical semigroups of a given genus},
journal = {Semigroup Forum},
year = {2010},
volume = {80},
number = {2},
pages = {242-254},
issn = {0037-1912},
affiliation = {Massachusetts Institute of Technology Department of Mathematics Cambridge MA USA},
doi = {10.1007/s00233-009-9190-9},
file = {:numericals/Zhao2010SF-Constructing.pdf:PDF},
keyword = {Mathematics and Statistics},
publisher = {Springer New York},
url = {https://dx.doi.org/10.1007/s00233-009-9190-9},
}
@Article{GeroldingerSchmid2017JoA-realization,
author = {Alfred Geroldinger and Wolfgang A. Schmid},
title = {A realization theorem for sets of distances},
journal = {Journal of Algebra},
year = {2017},
volume = {481},
pages = {188 - 198},
issn = {0021-8693},
doi = {https://doi.org/10.1016/j.jalgebra.2017.03.003},
file = {:numericals/GeroldingerSchmid2017JoA-realization.pdf:PDF},
keywords = {Krull monoids, Sets of lengths, Sets of distances },
url = {http://www.sciencedirect.com/science/article/pii/S0021869317301679},
}
@InCollection{DobbsMatthews2006,
author = {Dobbs, David E. and Matthews, Gretchen L.},
title = {On a question of {W}ilf concerning numerical semigroups},
booktitle = {Focus on commutative rings research},
publisher = {Nova Sci. Publ., New York},
year = {2006},
pages = {193--202},
file = {:numericals/DobbsMatthews2006.pdf:PDF},
mrclass = {20M14},
mrnumber = {2387753},
mrreviewer = {Pedro A. Garc\'\i a-S\'anchez},
}
@Article{DelgadoFarranGarcia-SanchezLlena2014ITIT-weight,
author = {Delgado, Manuel and Farr\'an, Jos\'e I. and Garc\'\i a-S\'anchez, Pedro A. and Llena, David},
title = {On the weight hierarchy of codes coming from semigroups with two generators},
journal = {IEEE Trans. Inform. Theory},
year = {2014},
volume = {60},
number = {1},
pages = {282--295},
issn = {0018-9448},
file = {:numericals/DelgadoFarranGarcia-SanchezLlena2014ITIT-weight.pdf:PDF},
fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
mrclass = {94B27},
mrnumber = {3150926},
mrreviewer = {Felice Manganiello},
url = {https://doi.org/10.1109/TIT.2013.2285217},
}
@Article{DelgadoFarranGarcia-SanchezLlena2013MC-generalized,
author = {Delgado, Manuel and Farr\'an, Jos\'e I. and Garc\'\i a-S\'anchez, Pedro A. and Llena, David},
title = {On the generalized {F}eng-{R}ao numbers of numerical semigroups generated by intervals},
journal = {Math. Comp.},
year = {2013},
volume = {82},
number = {283},
pages = {1813--1836},
issn = {0025-5718},
file = {:numericals/DelgadoFarranGarcia-SanchezLlena2013MC-generalized.pdf:PDF},
fjournal = {Mathematics of Computation},
mrclass = {20M14 (11T71 11Y55)},
mrnumber = {3042586},
mrreviewer = {Lance Eric Bryant},
url = {https://doi.org/10.1090/S0025-5718-2013-02673-7},
}
@Article{Eliahou2018JEMS-Wilfs,
author = {Eliahou, Shalom},
title = {Wilf’s conjecture and {M}acaulay’s theorem},
journal = {J. Eur. Math. Soc. (JEMS)},
year = {2018},
volume = {20},
number = {9},
pages = {2105--2129},
issn = {1435-9855},
doi = {10.4171/JEMS/807},
file = {:numericals/Eliahou2018JEMS-Wilfs.pdf:PDF},
fjournal = {Journal of the European Mathematical Society (JEMS)},
mrclass = {11B75 (05A10 05A20 13A02 20M14)},
mrnumber = {3836842},
url = {https://doi.org/10.4171/JEMS/807},
}
@Article{Sammartano2012SF-Numerical,
author = {Sammartano, Alessio},
title = {Numerical semigroups with large embedding dimension satisfy {W}ilf's conjecture},
journal = {Semigroup Forum},
year = {2012},
volume = {85},
number = {3},
pages = {439--447},
issn = {0037-1912},
doi = {10.1007/s00233-011-9370-2},
file = {:numericals/Sammartano2012SF-Numerical.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {3001594},
mrreviewer = {Lance Eric Bryant},
url = {https://doi.org/10.1007/s00233-011-9370-2},
}
@Article{Sylvester1984ET-Mathematical,
author = {Sylvester, J. J.},
title = {Mathematical questions with their solutions},
journal = {Educational Times},
year = {1884},
volume = {41},
pages = {21},
note = {Solution by W.J. Curran Sharp},
file = {:numericals/Sylvester1984ET-Mathematical.jpg:JPG image},
}
@PhdThesis{Dhayni2017phd-Problems,
author = {Dhayni, Mariam},
title = {Problems in numerical semigroups},
school = {Université d’Angers},
year = {2017},
file = {:/home/mdelgado/vida_universitaria/juris/2017-PhD-MariamDhayni/DHAYNI MARIAM THESE (1).pdf:PDF},
url = {https://www.theses.fr/2017ANGE0041.pdf},
}
@Article{Delgado2018MZ-question,
author = {Delgado, Manuel},
title = {On a question of {E}liahou and a conjecture of {W}ilf},
journal = {Math. Z.},
year = {2018},
volume = {288},
number = {1-2},
pages = {595--627},
issn = {0025-5874},
abstract = {To a numerical semigroup S, Eliahou associated a number{\$}{\$}{\{}{\{}{\backslash}mathrm{\{}E{\}}{\}}{\}}(S){\$}{\$} E(S) and proved that numerical semigroups for which the associated number is non negative satisfy Wilf's conjecture. The search for counterexamples for the conjecture of Wilf is therefore reduced to semigroups which have an associated negative Eliahou number. Eliahou mentioned 5 numerical semigroups whose Eliahou number is {\$}{\$}-1{\$}{\$} 1. The examples were discovered by Fromentin who observed that these are the only ones with negative Eliahou number among the over {\$}{\$}10^{\{}13{\}}{\$}{\$} 10^13 numerical semigroups of genus up to 60. We prove here that for any integer n there are infinitely many numerical semigroups S such that {\$}{\$}{\{}{\{}{\backslash}mathrm{\{}E{\}}{\}}{\}}(S)=n{\$}{\$} E(S) = n, by explicitly giving families of such semigroups. We prove that all the semigroups in these families satisfy Wilf's conjecture, thus providing not previously known examples of semigroups for which the conjecture holds.},
doi = {10.1007/s00209-017-1902-3},
file = {:numericals/Delgado2018MZ-question.pdf:PDF},
fjournal = {Mathematische Zeitschrift},
mrclass = {20M14 (05A20 11B75)},
mrnumber = {3774427},
url = {https://doi.org/10.1007/s00209-017-1902-3},
}
@InCollection{CziszterDomokosGeroldinger2016,
author = {Cziszter, K\'alm\'an and Domokos, M\'aty\'as and Geroldinger, Alfred},
title = {The interplay of invariant theory with multiplicative ideal theory and with arithmetic combinatorics},
booktitle = {Multiplicative ideal theory and factorization theory},
publisher = {Springer, [Cham]},
year = {2016},
volume = {170},
series = {Springer Proc. Math. Stat.},
pages = {43--95},
doi = {10.1007/978-3-319-38855-7_3},
file = {:/home/mdelgado/texto_springer/10.1007_978-3-319-38855-7.pdf:PDF},
mrclass = {13A50 (13A15 13F05 20M13)},
mrnumber = {3565804},
mrreviewer = {Ross P. Abraham},
url = {https://doi.org/10.1007/978-3-319-38855-7_3},
}
@Book{RosalesGarcia2009Book-Numerical,
title = {Numerical semigroups},
publisher = {Springer, New York},
year = {2009},
author = {Rosales, J. C. and García Sánchez, P. A.},
volume = {20},
series = {Developments in Mathematics},
isbn = {978-1-4419-0159-0},
doi = {10.1007/978-1-4419-0160-6},
file = {:numericals/RosalesGarcia2009Book-Numerical.pdf:PDF},
mrclass = {20M14},
mrnumber = {2549780},
pages = {x+181},
url = {http://dx.doi.org/10.1007/978-1-4419-0160-6},
}
@Article{Dhayni2018PJM-Wilfs,
author = {Dhayni, Mariam},
title = {Wilf’s conjecture for numerical semigroups},
journal = {Palest. J. Math.},
year = {2018},
volume = {7},
number = {2},
pages = {385--396},
issn = {2219-5688},
file = {:numericals/Dhayni2018PJM-Wilfs.pdf:PDF},
fjournal = {Palestine Journal of Mathematics},
mrclass = {11D07, 20M14},
}
@Article{Bras-AmorosFernandez-Gonzalez2018MC-Computation,
author = {Bras-Amor\'os, Maria and Fern\'andez-Gonz\'alez, Julio},
title = {Computation of numerical semigroups by means of seeds},
journal = {Math. Comp.},
year = {2018},
volume = {87},
number = {313},
pages = {2539--2550},
issn = {0025-5718},
doi = {10.1090/mcom/3292},
file = {:numericals/Bras-AmorosFernandez-Gonzalez2018MC-Computation.pdf:PDF},
fjournal = {Mathematics of Computation},
mrclass = {11B75 (05A15 06F05 20M14 68W30)},
mrnumber = {3802445},
url = {https://doi.org/10.1090/mcom/3292},
}
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author = {Backelin, J\"orgen},
title = {On the number of semigroups of natural numbers},
journal = {Math. Scand.},
year = {1990},
volume = {66},
number = {2},
pages = {197--215},
issn = {0025-5521},
doi = {10.7146/math.scand.a-12304},
file = {:numericals/Backelin1990MS-number.pdf:PDF},
fjournal = {Mathematica Scandinavica},
mrclass = {11N45 (11B13 20M14)},
mrnumber = {1075137},
mrreviewer = {John M. Howie},
url = {https://doi.org/10.7146/math.scand.a-12304},
}
@Article{Kaplan2017AMM-Counting,
author = {Kaplan, Nathan},
title = {Counting numerical semigroups},
journal = {Amer. Math. Monthly},
year = {2017},
volume = {124},
number = {9},
pages = {862--875},
issn = {0002-9890},
doi = {10.4169/amer.math.monthly.124.9.862},
file = {:numericals/Kaplan2017AMM-Counting.pdf:PDF},
fjournal = {American Mathematical Monthly},
mrclass = {20-02 (20M05)},
mrnumber = {3722042},
url = {https://doi.org/10.4169/amer.math.monthly.124.9.862},
}
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author = {Brauer, Alfred},
title = {On a problem of partitions},
journal = {Amer. J. Math.},
year = {1942},
volume = {64},
pages = {299--312},
issn = {0002-9327},
doi = {10.2307/2371684},
file = {:numericals/Brauer1942AJM-problem.pdf:PDF},
fjournal = {American Journal of Mathematics},
mrclass = {10.0X},
mrnumber = {0006196},
mrreviewer = {D. H. Lehmer},
url = {https://doi.org/10.2307/2371684},
}
@Article{Apery1946CRASP-Sur,
author = {Ap\'ery, Roger},
title = {Sur les branches superlin\'eaires des courbes alg\'ebriques},
journal = {C. R. Acad. Sci. Paris},
year = {1946},
volume = {222},
pages = {1198--1200},
file = {:numericals/Apery1946CRASP-Sur.pdf:PDF},
mrclass = {14.0X},
mrnumber = {0017942},
mrreviewer = {J. G. Semple},
}
@Article{HellusRechenauerWaldi2018SF-Note,
author = {Hellus, M. and Rechenauer, A. and Waldi, R.},
title = {Note on a theorem of Eliahou},
journal = {Semigroup Forum},
year = {2018},
volume = {97},
number = {1},
pages = {64--74},
month = {Aug},
issn = {1432-2137},
abstract = {From a result (Wilf's conjecture and Macaulay's theorem, 2017, Theorem 5.11) of Eliahou on the growth of the Hilbert function of a standard graded algebra we derive an inequality related to a question in Wilf (Am Math Mon 85, 1978). This enables us to construct a (to our knowledge new) class of numerical semigroups of embedding dimension 5 and arbitrarily high Cohen-Macaulay-type, for which the question of Wilf (1978) has an affirmative answer.},
day = {01},
doi = {10.1007/s00233-018-9923-8},
file = {:numericals/HellusRechenauerWaldi2018SF-Note.pdf:PDF},
url = {https://doi.org/10.1007/s00233-018-9923-8},
}
@Article{EliahouFromentin2019SF-misses,
author = {Eliahou, Shalom and Fromentin, Jean},
title = {Near-misses in {W}ilf's conjecture},
journal = {Semigroup Forum},
year = {2019},
volume = {98},
number = {2},
pages = {285--298},
issn = {0037-1912},
doi = {10.1007/s00233-018-9926-5},
file = {:numericals/EliahouFromentin2019SF-misses.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14 (05A99 11B75)},
mrnumber = {3917964},
url = {https://doi.org/10.1007/s00233-018-9926-5},
}
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title = {The {D}iophantine {F}robenius problem},
publisher = {Oxford University Press, Oxford},
year = {2005},
author = {Ramírez-Alfonsín, J. L.},
volume = {30},
series = {Oxford Lecture Series in Mathematics and its Applications},
isbn = {978-0-19-856820-9},
doi = {10.1093/acprof:oso/9780198568209.001.0001},
file = {:numericals/Ramirez-Alfonsin2005Book-Diophantine.pdf:PDF},
mrclass = {11D72 (05A17 11D04 11Y50 20M14)},
mrnumber = {2260521},
mrreviewer = {Ali Sinan Sert\"oz},
pages = {xvi+243},
url = {https://doi.org/10.1093/acprof:oso/9780198568209.001.0001},
}
@Book{GeroldingerHalter-Koch2006Book-Non,
title = {Non-unique factorizations},
publisher = {Chapman \& Hall/CRC, Boca Raton, FL},
year = {2006},
author = {Geroldinger, Alfred and Halter-Koch, Franz},
volume = {278},
series = {Pure and Applied Mathematics (Boca Raton)},
isbn = {978-1-58488-576-4; 1-58488-576-9},
note = {Algebraic, combinatorial and analytic theory},
doi = {10.1201/9781420003208},
file = {:factorization/GeroldingerHalter-Koch2006Book-Non.pdf:PDF},
mrclass = {20-02 (11-02 13-02)},
mrnumber = {2194494 (2006k:20001)},
mrreviewer = {W. Narkiewicz},
pages = {xxii+700},
url = {http://dx.doi.org/10.1201/9781420003208},
}
@InCollection{Geroldinger2009,
author = {Geroldinger, Alfred},
title = {Additive group theory and non-unique factorizations},
booktitle = {Combinatorial number theory and additive group theory},
publisher = {Birkh\"auser Verlag, Basel},
year = {2009},
series = {Adv. Courses Math. CRM Barcelona},
pages = {1--86},
doi = {10.1007/978-3-7643-8962-8},
file = {:factorization/Geroldinger2009.pdf:PDF},
mrclass = {20M14 (11A51 11B13 13A05)},
mrnumber = {2522037},
mrreviewer = {Fran\c{c}ois Hennecart},
url = {https://doi.org/10.1007/978-3-7643-8962-8},
}
@InCollection{GeroldingerHalter-Koch2006,
author = {Geroldinger, Alfred and Halter-Koch, Franz},
title = {Non-unique factorizations: a survey},
booktitle = {Multiplicative ideal theory in commutative algebra},
publisher = {Springer, New York},
year = {2006},
pages = {207--226},
doi = {10.1007/978-0-387-36717-0_13},
file = {:factorization/GeroldingerHalter-Koch2006-Survey.pdf:PDF},
mrclass = {20M14},
mrnumber = {2265810},
mrreviewer = {Alberto Facchini},
url = {https://doi.org/10.1007/978-0-387-36717-0_13},
}
@Article{FroebergGottliebHaeggkvist1987SF-numerical,
author = {Fr\"oberg, R. and Gottlieb, C. and H\"aggkvist, R.},
title = {On numerical semigroups},
journal = {Semigroup Forum},
year = {1987},
volume = {35},
number = {1},
pages = {63--83},
issn = {0037-1912},
doi = {10.1007/BF02573091},
file = {:numericals/FroebergGottliebHaeggkvist1987SF-numerical.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14 (11B13)},
mrnumber = {880351},
mrreviewer = {John M. Howie},
url = {https://doi.org/10.1007/BF02573091},
}
@Article{KunzWaldi2017JA-deviation,
author = {Kunz, E. and Waldi, R.},
title = {On the deviation and the type of certain local {C}ohen-{M}acaulay rings and numerical semigroups},
journal = {J. Algebra},
year = {2017},
volume = {478},
pages = {397--409},
issn = {0021-8693},
doi = {10.1016/j.jalgebra.2017.01.041},
file = {:numericals/KunzWaldi2017JA-deviation.pdf:PDF},
fjournal = {Journal of Algebra},
mrclass = {13H10 (11D07)},
mrnumber = {3621681},
mrreviewer = {Alessio Sammartano},
url = {https://doi.org/10.1016/j.jalgebra.2017.01.041},
}
@Article{MoscarielloSammartano2015MZ-conjecture,
author = {Moscariello, Alessio and Sammartano, Alessio},
title = {On a conjecture by {W}ilf about the {F}robenius number},
journal = {Math. Z.},
year = {2015},
volume = {280},
number = {1-2},
pages = {47--53},
issn = {0025-5874},
doi = {10.1007/s00209-015-1412-0},
file = {:numericals/MoscarielloSammartano2015MZ-conjecture.pdf:PDF},
fjournal = {Mathematische Zeitschrift},
mrclass = {11D07 (11B75 20M14)},
mrnumber = {3343897},
mrreviewer = {Ali Sinan Sert\"oz},
url = {https://doi.org/10.1007/s00209-015-1412-0},
}
@Article{BarucciStrazzanti2019SF-Dilatations,
author = {Barucci, V. and Strazzanti, F.},
title = {Dilatations of numerical semigroups},
journal = {Semigroup Forum},
year = {2019},
volume = {98},
number = {2},
pages = {251--260},
issn = {0037-1912},
file = {:numericals/BarucciStrazzanti2019SF-Dilatations.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {3917961},
url = {https://doi.org/10.1007/s00233-018-9922-9},
}
@Article{BlancoGarcia-SanchezPuerto2011IJAC-Counting,
author = {Blanco, V\'{i}ctor and Garc\'{i}a-S\'{a}nchez, Pedro A. and Puerto, Justo},
title = {Counting numerical semigroups with short generating functions},
journal = {Internat. J. Algebra Comput.},
year = {2011},
volume = {21},
number = {7},
pages = {1217--1235},
issn = {0218-1967},
doi = {10.1142/S0218196711006911},
file = {:numericals/BlancoGarcia-SanchezPuerto2011IJAC-Counting.pdf:PDF},
fjournal = {International Journal of Algebra and Computation},
mrclass = {20M14 (05A15 11D45)},
mrnumber = {2863434},
mrreviewer = {Thomas Kahle},
url = {https://doi.org/10.1142/S0218196711006911},
}
@Article{BlancoRosales2012SF-set,
author = {Blanco, V. and Rosales, J. C.},
title = {The set of numerical semigroups of a given genus},
journal = {Semigroup Forum},
year = {2012},
volume = {85},
number = {2},
pages = {255--267},
issn = {0037-1912},
doi = {10.1007/s00233-012-9378-2},
file = {:numericals/BlancoRosales2012SF-set.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14 (05A15 05C05)},
mrnumber = {2969049},
mrreviewer = {Lance Eric Bryant},
url = {https://doi.org/10.1007/s00233-012-9378-2},
}
@InCollection{Barucci2009,
author = {Barucci, Valentina},
title = {On propinquity of numerical semigroups and one-dimensional local {C}ohen {M}acaulay rings},
booktitle = {Commutative algebra and its applications},
publisher = {Walter de Gruyter, Berlin},
year = {2009},
pages = {49--60},
file = {:numericals/Barucci2009-Propinquity.pdf:PDF},
mrclass = {20M14 (13A15 13H10)},
mrnumber = {2606276},
mrreviewer = {Michael A. Freeze},
}
@Article{Garcia-GarciaMarin-AragonVigneron-Tenorio2018SF-extension,
author = {Garc\'{i}a-Garc\'{i}a, J. I. and Mar\'{i}n-Arag\'{o}n, D. and Vigneron-Tenorio, A.},
title = {An extension of {W}ilf's conjecture to affine semigroups},
journal = {Semigroup Forum},
year = {2018},
volume = {96},
number = {2},
pages = {396--408},
issn = {0037-1912},
doi = {10.1007/s00233-017-9906-1},
file = {:numericals/Garcia-GarciaMarin-AragonVigneron-Tenorio2018SF-extension.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14 (11B75)},
mrnumber = {3782650},
url = {https://doi.org/10.1007/s00233-017-9906-1},
}
@Article{BernardiniTorres2017DM-Counting,
author = {Bernardini, Matheus and Torres, Fernando},
title = {Counting numerical semigroups by genus and even gaps},
journal = {Discrete Math.},
year = {2017},
volume = {340},
number = {12},
pages = {2853--2863},
issn = {0012-365X},
doi = {10.1016/j.disc.2017.08.001},
file = {:numericals/BernardiniTorres2017DM-Counting.pdf:PDF},
fjournal = {Discrete Mathematics},
mrclass = {20M14 (05A15 05A16)},
mrnumber = {3698073},
mrreviewer = {Yanfeng Luo},
url = {https://doi.org/10.1016/j.disc.2017.08.001},
}
@Article{BarucciFroeberg1997JA-One-dimensional,
author = {Barucci, Valentina and Fr\"{o}berg, Ralf},
title = {One-dimensional almost {G}orenstein rings},
journal = {J. Algebra},
year = {1997},
volume = {188},
number = {2},
pages = {418--442},
issn = {0021-8693},
doi = {10.1006/jabr.1996.6837},
file = {:numericals/BarucciFroeberg1997JA-One-dimensional.pdf:PDF},
fjournal = {Journal of Algebra},
mrclass = {13H10 (13B15)},
mrnumber = {1435367},
mrreviewer = {Ngo Viet Trung},
url = {https://doi.org/10.1006/jabr.1996.6837},
}
@Article{Kunz2016SF-type,
author = {Kunz, E.},
title = {On the type of certain numerical semigroups and a question of {W}ilf},
journal = {Semigroup Forum},
year = {2016},
volume = {93},
number = {1},
pages = {205--210},
issn = {0037-1912},
doi = {10.1007/s00233-015-9755-8},
file = {:numericals/Kunz2016SF-type.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {3528437},
mrreviewer = {Paula M. Machado Cruz Catarino},
url = {https://doi.org/10.1007/s00233-015-9755-8},
}
@Book{TaoVu2006Book-Additive,
title = {Additive combinatorics},
publisher = {Cambridge University Press, Cambridge},
year = {2006},
author = {Tao, Terence and Vu, Van},
volume = {105},
series = {Cambridge Studies in Advanced Mathematics},
isbn = {978-0-521-85386-6; 0-521-85386-9},
doi = {10.1017/CBO9780511755149},
file = {:numericals/TaoVu2006Book-Additive.pdf:PDF},
mrclass = {11-02 (05-02 05D10 11B13 11P70 11P82 28D05 37A45)},
mrnumber = {2289012},
mrreviewer = {Serge\u{\i} V. Konyagin},
pages = {xviii+512},
url = {https://doi.org/10.1017/CBO9780511755149},
}
@Article{Matthews2005I-integers,
author = {Matthews, Gretchen L.},
title = {On integers nonrepresentable by a generalized arithmetic progression},
journal = {Integers},
year = {2005},
volume = {5},
number = {2},
pages = {A12, 6},
issn = {1553-1732},
file = {:numericals/Matthews2005I-integers.pdf:PDF},
fjournal = {Integers. Electronic Journal of Combinatorial Number Theory},
mrclass = {11B25},
mrnumber = {2192090},
}
@Article{Curtis1990MS-formulas,
author = {Curtis, Frank},
title = {On formulas for the {F}robenius number of a numerical semigroup},
journal = {Math. Scand.},
year = {1990},
volume = {67},
number = {2},
pages = {190--192},
issn = {0025-5521},
doi = {10.7146/math.scand.a-12330},
file = {:numericals/Curtis1990MS-formulas.pdf:PDF},
fjournal = {Mathematica Scandinavica},
mrclass = {11D04 (20M05)},
mrnumber = {1096454},
mrreviewer = {Edward L. Cohen},
url = {https://doi.org/10.7146/math.scand.a-12330},
}
@Article{SzemerediVu2006JAMS-Long,
author = {Szemer\'{e}di, E. and Vu, V.},
title = {Long arithmetic progressions in sumsets: thresholds and bounds},
journal = {J. Amer. Math. Soc.},
year = {2006},
volume = {19},
number = {1},
pages = {119--169},
issn = {0894-0347},
doi = {10.1090/S0894-0347-05-00502-3},
file = {:numericals/SzemerediVu2006JAMS-Long.pdf:PDF},
fjournal = {Journal of the American Mathematical Society},
mrclass = {11B25 (11B75 11P70)},
mrnumber = {2169044},
mrreviewer = {Ben Joseph Green},
url = {https://doi.org/10.1090/S0894-0347-05-00502-3},
}
@Article{SzemerediVu2006AoM2-Finite,
author = {Szemer\'{e}di, E. and Vu, V. H.},
title = {Finite and infinite arithmetic progressions in sumsets},
journal = {Ann. of Math. (2)},
year = {2006},
volume = {163},
number = {1},
pages = {1--35},
issn = {0003-486X},
doi = {10.4007/annals.2006.163.1},
file = {:numericals/SzemerediVu2006AoM2-Finite.pdf:PDF},
fjournal = {Annals of Mathematics. Second Series},
mrclass = {11B25 (05D05)},
mrnumber = {2195131},
mrreviewer = {Ben Joseph Green},
url = {https://doi.org/10.4007/annals.2006.163.1},
}
@Article{SzemerediVu2005PLMS3-Long,
author = {Szemer\'{e}di, E. and Vu, V. H.},
title = {Long arithmetic progressions in sum-sets and the number of {$x$}-sum-free sets},
journal = {Proc. London Math. Soc. (3)},
year = {2005},
volume = {90},
number = {2},
pages = {273--296},
issn = {0024-6115},
doi = {10.1112/S0024611504015059},
file = {:numericals/SzemerediVu2005PLMS3-Long.pdf:PDF},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
mrclass = {11B25 (05A16)},
mrnumber = {2142128},
mrreviewer = {Ben Joseph Green},
url = {https://doi.org/10.1112/S0024611504015059},
}
@Article{Lev2010AMH-Consecutive,
author = {Lev, V. F.},
title = {Consecutive integers in high-multiplicity sumsets},
journal = {Acta Math. Hungar.},
year = {2010},
volume = {129},
number = {3},
pages = {245--253},
issn = {0236-5294},
doi = {10.1007/s10474-010-0026-6},
file = {:numericals/Lev2010AMH-Consecutive.pdf:PDF},
fjournal = {Acta Mathematica Hungarica},
mrclass = {11B13 (11B25 11B75 11P70)},
mrnumber = {2737725},
mrreviewer = {Radhakrishnan Nair},
url = {https://doi.org/10.1007/s10474-010-0026-6},
}
@Article{Li2015CM-Effective,
author = {Li, Han},
title = {Effective limit distribution of the {F}robenius numbers},
journal = {Compos. Math.},
year = {2015},
volume = {151},
number = {5},
pages = {898--916},
issn = {0010-437X},
doi = {10.1112/S0010437X14007866},
file = {:numericals/Li2015CM-Effective.pdf:PDF},
fjournal = {Compositio Mathematica},
mrclass = {37A25 (11B57 11D07 11H06 11K31)},
mrnumber = {3347994},
mrreviewer = {Poj Lertchoosakul},
url = {https://doi.org/10.1112/S0010437X14007866},
}
@Article{ONeillPelayo2018AiAM-Apery,
author = {O'Neill, Christopher and Pelayo, Roberto},
title = {Ap\'{e}ry sets of shifted numerical monoids},
journal = {Adv. in Appl. Math.},
year = {2018},
volume = {97},
pages = {27--35},
issn = {0196-8858},
doi = {10.1016/j.aam.2018.01.005},
file = {:numericals/ONeillPelayo2018AiAM-Apery.pdf:PDF},
fjournal = {Advances in Applied Mathematics},
mrclass = {20M14 (11D07)},
mrnumber = {3777345},
mrreviewer = {Alessio Sammartano},
unknown = {O'Neill, Christopher and Pelayo, Roberto},
url = {https://doi.org/10.1016/j.aam.2018.01.005},
}
@Article{FaillaPetersonUtano2016SF-Algorithms,
author = {Failla, Gioia and Peterson, Chris and Utano, Rosanna},
title = {Algorithms and basic asymptotics for generalized numerical semigroups in {$\Bbb{N}^d$}},
journal = {Semigroup Forum},
year = {2016},
volume = {92},
number = {2},
pages = {460--473},
issn = {0037-1912},
doi = {10.1007/s00233-015-9690-8},
file = {:numericals/FaillaPetersonUtano2016SF-Algorithms.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14 (68W05)},
mrnumber = {3472026},
mrreviewer = {Paula Murgel Veloso},
url = {https://doi.org/10.1007/s00233-015-9690-8},
}
@Article{RosalesGarcia-SanchezGarcia-GarciaJimenezMadrid2003SF-oversemigroups,
author = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'{e}nez Madrid, J. A.},
title = {The oversemigroups of a numerical semigroup},
journal = {Semigroup Forum},
year = {2003},
volume = {67},
number = {1},
pages = {145--158},
issn = {0037-1912},
doi = {10.1007/s00233-002-0007-3},
file = {:numericals/RosalesGarcia-SanchezGarcia-GarciaJimenezMadrid2003SF-oversemigroups.pdf:PDF},
fjournal = {Semigroup Forum},
mrclass = {20M14},
mrnumber = {1978528},
mrreviewer = {Attila Nagy},
url = {https://doi.org/10.1007/s00233-002-0007-3},
}
@Article{EliahouFromentin2020JCTSA-Gapsets,
author = {Eliahou, Shalom and Fromentin, Jean},
title = {Gapsets and numerical semigroups},
journal = {J. Combin. Theory Ser. A},
year = {2020},
volume = {169},
pages = {105129, 19},
issn = {0097-3165},
doi = {10.1016/j.jcta.2019.105129},
file = {:numericals/EliahouFromentin2020JCTSA-Gapsets.pdf:PDF},
fjournal = {Journal of Combinatorial Theory. Series A},
mrclass = {20M14},
mrnumber = {3998824},
mrreviewer = {Alberto Vigneron-Tenorio},
url = {https://doi.org/10.1016/j.jcta.2019.105129},
}
@Article{RosalesGarcia-SanchezGarcia-GarciaJimenezMadrid2004JPAA-Fundamental,
author = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'{e}nez Madrid, J. A.},
title = {Fundamental gaps in numerical semigroups},
journal = {J. Pure Appl. Algebra},
year = {2004},
volume = {189},
number = {1-3},
pages = {301--313},
issn = {0022-4049},
doi = {10.1016/j.jpaa.2003.10.024},
file = {:numericals/RosalesGarcia-SanchezGarcia-GarciaJimenezMadrid2004JPAA-Fundamental.pdf:PDF},
fjournal = {Journal of Pure and Applied Algebra},
mrclass = {20M14},
mrnumber = {2038577},
url = {https://doi.org/10.1016/j.jpaa.2003.10.024},
}
@Article{Robles-PerezRosales2008AMB-Equivalent,
author = {Robles-P\'{e}rez, Aureliano M. and Rosales, Jos\'{e} Carlos},
title = {Equivalent proportionally modular {D}iophantine inequalities},
journal = {Arch. Math. (Basel)},
year = {2008},
volume = {90},
number = {1},
pages = {24--30},
issn = {0003-889X},
doi = {10.1007/s00013-007-2379-9},
file = {:numericals/Robles-PerezRosales2008AMB-Equivalent.pdf:PDF},
fjournal = {Archiv der Mathematik},
mrclass = {20M14 (11D75)},