xref: /dports/math/gap/gap-4.11.0/pkg/NumericalSgps-1.2.1/doc/NumericalSgps.bib

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@article {RGGJ04,
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@Article{CGLPR,
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@Article{CGL,
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  FJOURNAL = {Mathematics of Computation},
    VOLUME = {86},
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    NUMBER = {307},
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      ISSN = {0025-5718},
   MRCLASS = {20M14 (11Y11 68W40)},
  MRNUMBER = {3647965},
       DOI = {10.1090/mcom/3160},
       URL = {https://doi.org/10.1090/mcom/3160},
}

@article{GG-MF-VT,
AUTHOR = {Garc\'{\i}a-Garc\'{\i}a, J. I. and Moreno-Fr\'{\i}as, M. A. and Vigneron-Tenorio, A.},
TITLE = {Computation of Delta sets of numerical monoids},
JOURNAL = {Monatsh. Math. },
VOLUME = {178},
PAGES={457--472},
YEAR ={2015},
}

@misc{Normaliz,
AUTHOR={Bruns, W. and  Ichim, B. and  R\"omer, T.  and  S\"oger C.},
TITLE={Normaliz. Algorithms for rational cones and affine monoids},
YEAR={2014},
VERSION={2.12},
howpublished={\url{http://www.math.uos.de/normaliz}},
}

@misc{Singular,
 title = {{\sc Singular} {3-1-6} --- {A} computer algebra system for polynomial computations},
 author = {Decker, Wolfram and Greuel, Gert-Martin and Pfister, Gerhard and Sch\"onemann, Hans},
 year = {2012},
 howpublished = {\url{http://www.singular.uni-kl.de}},
}

@misc{NmzInterface,
author={Gutsche, S and  Horn, M. and  S\"oger, C.},
title={NormalizInterface for GAP},
year={2014},
howpublished={\url{https://github.com/fingolfin/NormalizInterface}},
}

@misc{SingularInterface,
author={Barakat, M. and  Horn, M. and  Lübeck, F.  and Motsak, O. and  Neunhoeffer, M. and  Schoenemann H.},
title={SingularInterface for GAP},
year={2014},
howpublished={\url{https://github.com/gap-system/SingularInterface.git}},
}

@misc{Singularpackage,
author={Costantini, M. and  de Graaf, W.},
year={2012},
title={GAP package singular; the GAP interface to Singular},
howpublished={\url{http://gap-system.org/Packages/singular.html}},
}

@article{R-GS-GG-B,
author = {Rosales,J. C. and Garc\'{\i}a-S\'anchez,P. A. and, Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.},
title = {SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS},
journal = {Journal of the London Mathematical Society},
volume = {65},
issue = {03},
month = {6},
year = {2002},
issn = {1469-7750},
pages = {611--623},
numpages = {13},
doi = {10.1112/S0024610701003052},
URL = {http://journals.cambridge.org/article_S0024610701003052},
}

@article{R-GS,
title = "Nonnegative elements of subgroups of \(\mathbb{Z}^n\)",
journal = "Linear Algebra and its Applications ",
volume = "270",
number = "1-3",
pages = "351- 357",
year = "1998",
note = "",
issn = "0024-3795",
doi = "http://dx.doi.org/10.1016/S0024-3795(97)00309-1",
url = "http://www.sciencedirect.com/science/article/pii/S0024379597003091",
author = "J.C. Rosales and Pedro A. Garc\'{\i}a-S\'anchez",
abstract = "We give a method to compute all nonnegative integer solutions of a homogeneous system of linear equations. We use this method to provide an algorithm to compute all nonnegative integer solutions of homogeneous systems of equations having some of the equations in congruences. "
}

@article {MR1678508,
    AUTHOR = {Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {On free affine semigroups},
   JOURNAL = {Semigroup Forum},
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      YEAR = {1999},
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     CODEN = {SMGFAN},
   MRCLASS = {13C40 (20M14)},
  MRNUMBER = {1678508 (2000j:13020)},
MRREVIEWER = {L{\^e} Tu{\^a}n Hoa},
       DOI = {10.1007/BF03325435},
       URL = {http://dx.doi.org/10.1007/BF03325435},
}

@article {MR0269762,
    AUTHOR = {Herzog, J{\"u}rgen},
     TITLE = {Generators and relations of abelian semigroups and semigroup
              rings. },
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {3},
      YEAR = {1970},
     PAGES = {175--193},
      ISSN = {0025-2611},
   MRCLASS = {20.93},
  MRNUMBER = {0269762 (42 \#4657)},
MRREVIEWER = {J. B. Kim},
}

@article {MR1394747,
    AUTHOR = {Eisenbud, David and Sturmfels, Bernd},
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   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {84},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {1--45},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {13P10 (13A30 14M25)},
  MRNUMBER = {1394747 (97d:13031)},
MRREVIEWER = {P. Schenzel},
       DOI = {10.1215/S0012-7094-96-08401-X},
       URL = {http://dx.doi.org/10.1215/S0012-7094-96-08401-X},
}
@Misc{4ti2,
  author =   {4ti2 team},
  title =    {4ti2---A software package for algebraic, geometric and
              combinatorial problems on linear spaces},
  howpublished = {{A}vailable at www.4ti2.de}
}

@Misc{4ti2Interface,
  author =   {S. Gutsche},
  title =    {4ti2Interface, A link to 4ti2},
  howpublished = {\url{http://www.gap-system.org/Packages/4ti2interface.html}}
}

@misc{ GradedModules,
  author =           {Barakat,   M.   and   Gutsche,   S.   and  Jambor,  S.  and
                      Lange-Hegermann, M. and Lorenz, A. and Motsak, O.},
  title =            {{GradedModules},  A  homalg  based  package for the Abelian
                      category   of   finitely   presented  graded  modules  over
                      computable graded rings, {V}ersion 2014.09.17},
  month =            {Sep},
  year =             {2014},
  note =             {GAP package},
  howpublished =     {\href
                      {http://homalg.math.rwth-aachen.de/~barakat/homalg-project/Gr\
adedModules/}
                      {\texttt{http://homalg.math.rwth-aachen.de/}\discretionary
                      {}{}{}\texttt{\texttt{\symbol{126}}barakat/}\discretionary
                      {}{}{}\texttt{homalg-project/}\discretionary
                      {}{}{}\texttt{GradedModules/}}},
  keywords =         {modules;  graded modules; graduation; multi-graded modules;
                      Tate resolution},
  printedkey =       {BGJLLM14}
}

@article{DGSRP15,
   author = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P.~A. and Robles-P{\'e}rez, A.~M.},
    title = {Numerical semigroups with a given set of pseudo-Frobenius numbers},
  journal = {LMS J. Comput. Math.},
 keywords = {Mathematics - Commutative Algebra, Mathematics - Combinatorics, 11D07, 20M14, 20-04},
     year = {2016},
     volume= {19},
     pages={186--205}
}

@article{GSONW,
AUTHOR = {Garc\'{\i}a-S\'anchez, P. A. and O'Neill, C. and Webb, G.},
TITLE = {On the computation of factorization invariants for affine semigroups},
JOURNAL = {arxiv:1504.02998},
YEAR ={2017},
URL= {http://arxiv.org/abs/1504.02998},
}

@article {E,
    AUTHOR = {Eliahou, Shalom},
     TITLE = {Wilf's conjecture and {M}acaulay's theorem},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {20},
      YEAR = {2018},
    NUMBER = {9},
     PAGES = {2105--2129},
      ISSN = {1435-9855},
   MRCLASS = {11B75 (05A10 05A20 13A02 20M14)},
  MRNUMBER = {3836842},
       DOI = {10.4171/JEMS/807},
       URL = {https://doi.org/10.4171/JEMS/807},
}


@article {Wilf,
    AUTHOR = {Wilf, Herbert S.},
     TITLE = {A circle-of-lights algorithm for the ``money-changing
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   JOURNAL = {Amer. Math. Monthly},
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    NUMBER = {7},
     PAGES = {562--565},
      ISSN = {0002-9890},
   MRCLASS = {10A30 (05A17 68A10)},
  MRNUMBER = {0556658 (58 \#27728)},
MRREVIEWER = {Dennis White},
}

@article {Stokes,
    AUTHOR = {Stokes, Klara},
     TITLE = {Patterns of ideals of numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {93},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {180--200},
      ISSN = {0037-1912},
   MRCLASS = {20M14 (11D07 20M12)},
  MRNUMBER = {3528435},
MRREVIEWER = {Andreas Reinhart},
       DOI = {10.1007/s00233-015-9741-1},
       URL = {https://doi.org/10.1007/s00233-015-9741-1},
}

@article {K-W,
    AUTHOR = {Kunz, E. and Waldi, R.},
     TITLE = {Geometrical illustration of numerical semigroups and of some
              of their invariants},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {89},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {664--691},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3274840},
MRREVIEWER = {Kurt D. Herzinger},
       DOI = {10.1007/s00233-014-9599-7},
       URL = {http://dx.doi.org/10.1007/s00233-014-9599-7},
}

@article {DGSM,
    AUTHOR = {D'Anna, Marco and Garc\'{\i}a-S\'{a}nchez, Pedro A. and Micale,
              Vincenzo and Tozzo, Laura},
     TITLE = {Good subsemigroups of {$\Bbb N^n$}},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {28},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {179--206},
      ISSN = {0218-1967},
   MRCLASS = {20M14},
  MRNUMBER = {3786416},
       DOI = {10.1142/S0218196718500091},
       URL = {https://doi.org/10.1142/S0218196718500091},
}

@article {MC-O-T,
    AUTHOR = {M{\'a}rquez-Campos, Guadalupe and Ojeda, Ignacio and Tornero,
              Jos{\'e} M.},
     TITLE = {On the computation of the {A}p\'ery set of numerical monoids
              and affine semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {91},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {139--158},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3369384},
MRREVIEWER = {Andreas Reinhart},
       DOI = {10.1007/s00233-014-9631-y},
       URL = {http://dx.doi.org/10.1007/s00233-014-9631-y},
}


@article {Roune,
    AUTHOR = {Roune, Bjarke Hammersholt},
     TITLE = {Solving thousand-digit {F}robenius problems using {G}r\"obner
              bases},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {43},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--7},
      ISSN = {0747-7171},
   MRCLASS = {13P10 (13D40 68W30)},
  MRNUMBER = {2381966},
MRREVIEWER = {Giancarlo Rinaldo},
       DOI = {10.1016/j.jsc.2007.06.002},
       URL = {http://dx.doi.org/10.1016/j.jsc.2007.06.002},
}

@article{Ugolini,
author = {Ugolini, Simone},
title = {On numerical semigroups closed with respect to the action of affine maps},
journal= "arXiv",
volume= "1505.06580",
year= "2016"
}

@article {MR3493240,
    AUTHOR = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {{numericalsgps}, a {GAP} package for numerical
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   JOURNAL = {ACM Commun. Comput. Algebra},
  FJOURNAL = {ACM Communications in Computer Algebra},
    VOLUME = {50},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {12--24},
      ISSN = {1932-2232},
   MRCLASS = {20-04 (20M14 68W30)},
  MRNUMBER = {3493240},
}

@article {arf-frob-gen,
  AUTHOR={Garc{\'{\i}}a-S{\'a}nchez, P. A. and  Heredia, B. A. and Karakas, H. I. and Rosales, J. C.},
  TITLE = {Parametrizing Arf numerical semigroups},
  JOURNAL = {J. Algebra Appl.},
  VOLUME = {16},
  YEAR = {2017},
  PAGES = {1750209 (31 pages)}
}

@article {duplication,
    AUTHOR = {D'Anna, M. and Strazzanti, F.},
     TITLE = {The numerical duplication of a numerical semigroup},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {87},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {149--160},
      ISSN = {0037-1912},
   MRCLASS = {20M12 (06B10 13A15 13A30 13F10 16D25)},
  MRNUMBER = {3079777},
MRREVIEWER = {Paula M. Machado Cruz Catarino},
       DOI = {10.1007/s00233-012-9451-x},
       URL = {http://dx.doi.org/10.1007/s00233-012-9451-x},
}

@article {DA-G-H,
	AUTHOR = {D'Anna, Marco and Guerrieri, Anna and Heinzer, William},
	TITLE = {Invariants of ideals having principal reductions},
	JOURNAL = {Comm. Algebra},
	FJOURNAL = {Communications in Algebra},
	VOLUME = {29},
	YEAR = {2001},
	NUMBER = {2},
	PAGES = {889--906},
	ISSN = {0092-7872},
	MRCLASS = {13A15 (13C10)},
	MRNUMBER = {1842007},
	MRREVIEWER = {L. J. Ratliff, Jr.},
	DOI = {10.1081/AGB-100001550},
	URL = {http://dx.doi.org/10.1081/AGB-100001550},
}

@article {Br-acute,
    AUTHOR = {Bras-Amor\'os, Maria},
     TITLE = {Acute semigroups, the order bound on the minimum distance, and
              the {F}eng-{R}ao improvements},
   JOURNAL = {IEEE Trans. Inform. Theory},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Information Theory},
    VOLUME = {50},
      YEAR = {2004},
    NUMBER = {6},
     PAGES = {1282--1289},
      ISSN = {0018-9448},
   MRCLASS = {20M14 (94B27)},
  MRNUMBER = {2094884},
       DOI = {10.1109/TIT.2004.828104},
       URL = {http://dx.doi.org/10.1109/TIT.2004.828104},
}


@article {A-A-GS,
	AUTHOR = {Abbas, A. and Assi, A. and García-Sánchez, P. A.},
	TITLE = {Canonical bases of modules over one dimensional k-algebras},
JOURNAL = {arxiv:1703.02825},
YEAR ={2017},
URL= {http://arxiv.org/abs/1703.02825},
}

@Article{DelgadoFarranGarcia-SanchezLlena2013MC,
  Title                    = {{On the generalized Feng-Rao numbers of numerical semigroups generated by intervals}},
  Author                   = {{Delgado}, M. and {Farr{\'a}n}, J.~I. and {Garc{\'{\i}}a-S{\'a}nchez}, P.~A. and {Llena}, D.},
  Journal                  = {Mathematics of Computation},
  Year                     = {2013},
  Number                   = {283},
  Pages                    = {1813--1836},
  Volume                   = {82},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/2011arXiv1105.4833D},
  Archiveprefix            = {arXiv},
  Doi                      = {http://dx.doi.org/10.1090/S0025-5718-2013-02673-7},
  Eprint                   = {1105.4833},
  Keywords                 = {Mathematics - Number Theory, 20M14, 11Y55, 11T71},
  Primaryclass             = {math.NT}
}


@article{BOR18,
    AUTHOR = {Branco, M. and  Ojeda, I. and Rosales, J. C.},
     TITLE = {Almost symmetric numerical semigroups with a given Frobenus number and type},
   JOURNAL = {preprint},
      YEAR = {2018},
}

@article{C-F-U,
author={Cisto, C. and Failla, G. and Utano R.},
title={On the generators of a generalized numerical semigroup},
journal={Analele Stiintifice ale Universitatii Ovidius Constanta},
year={2018},
}


@article {G-K,
	AUTHOR = {Matsuoka, N. and Kumashiro, S.},
	TITLE = {The generalized Gorenstein property and numerical semigroup rings obtained by gluing},
JOURNAL = {IMNS2010 - abstracts},
YEAR ={2017},
URL= {https://www.ugr.es/~imns2010/2018/Talks/NMatsuoka.pdf},
}

@ARTICLE{G-I-K-T,
   author = {{Goto}, S. and {Isobe}, R. and {Kumashiro}, S. and {Taniguchi}, N.
	},
    title = "{Characterization of generalized Gorenstein rings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1704.08901},
 primaryClass = "math.AC",
 keywords = {Mathematics - Commutative Algebra, 13H10, 13H15, 13A30},
     year = 2017,
    month = apr,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170408901G},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {M00,
    AUTHOR = {Moree, P.},
     TITLE = {Approximation of singular series and automata},
      NOTE = {With an appendix by Gerhard Niklasch},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {101},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {385--399},
      ISSN = {0025-2611},
   MRCLASS = {11Y60 (11Y35)},
  MRNUMBER = {1751040},
MRREVIEWER = {M. Ram Murty},
       DOI = {10.1007/s002290050222},
       URL = {https://doi.org/10.1007/s002290050222},
}


@article {C-GS-M,
    AUTHOR = {Ciolan, Emil-Alexandru and Garc\'{i}a-S\'{a}nchez, Pedro A. and Moree,
              Pieter},
     TITLE = {Cyclotomic numerical semigroups},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {30},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {650--668},
      ISSN = {0895-4801},
   MRCLASS = {20M14 (11B68 11C08)},
  MRNUMBER = {3483156},
MRREVIEWER = {Alessio Moscariello},
       DOI = {10.1137/140989479},
       URL = {https://doi.org/10.1137/140989479},
}

@article{C-GS-HP-M,
    AUTHOR = {Ciolan, Emil-Alexandru and Garc\'{i}a-S\'{a}nchez, Pedro A. and Herrera-Poyatos, And\'es and Moree,
              Pieter},
     TITLE = {Cyclotomic exponent sequences of numerical semigroups},
   JOURNAL = {preprint},
      YEAR = {2019},
}


Citation to include in documentation:
@Article{M-Z,
author = {{Maugeri}, Nicola and {Zito}, Giuseppe},
title = "{Embedding dimension of a good semigroup}",
journal = {arXiv e-prints},
keywords = {Mathematics - Commutative Algebra, 20-04, 13A18, 13H99, 20M14, 14H50},
year = "2019",
month = "Mar",
eid = {arXiv:1903.02057},
pages = {arXiv:1903.02057},
archivePrefix = {arXiv},
eprint = {1903.02057},
primaryClass = {math.AC},
adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190302057M},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {B-DA-F-1,
    AUTHOR = {Barucci, V. and D'Anna, M. and Fr\"{o}berg, R.},
     TITLE = {The semigroup of values of a one-dimensional local ring with
              two minimal primes},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {28},
      YEAR = {2000},
    NUMBER = {8},
     PAGES = {3607--3633},
      ISSN = {0092-7872},
   MRCLASS = {13H10 (13A18 13B22 20M14)},
  MRNUMBER = {1767576},
MRREVIEWER = {Marco Fontana},
       DOI = {10.1080/00927870008827044},
       URL = {https://doi.org/10.1080/00927870008827044},
}

@article {B-DA-F-2,
    AUTHOR = {Barucci, V. and D'Anna, M. and Fr\"{o}berg, R.},
     TITLE = {Analytically unramified one-dimensional semilocal rings and
              their value semigroups},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {147},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {215--254},
      ISSN = {0022-4049},
   MRCLASS = {13H99 (13A18)},
  MRNUMBER = {1747441},
MRREVIEWER = {Ngo Viet Trung},
       DOI = {10.1016/S0022-4049(98)00160-1},
       URL = {https://doi.org/10.1016/S0022-4049(98)00160-1},
}

@article {DM,
    AUTHOR = {Delgado de la Mata, F\'{e}lix},
     TITLE = {Gorenstein curves and symmetry of the semigroup of values},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {61},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {285--296},
      ISSN = {0025-2611},
   MRCLASS = {14H20 (13H10 13J10)},
  MRNUMBER = {949819},
MRREVIEWER = {J\"{u}rgen Herzog},
       DOI = {10.1007/BF01258440},
       URL = {https://doi.org/10.1007/BF01258440},
}


@ARTICLE{BOR19,
       author = {{Branco}, M.~B. and {Ojeda}, I. and {Rosales}, J.~C.},
        title = "{The set of numerical semigroups of a given multiplicity and Frobenius number}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Group Theory, 20M14, 11D07},
         year = "2019",
        month = "Apr",
          eid = {arXiv:1904.05551},
        pages = {arXiv:1904.05551},
archivePrefix = {arXiv},
       eprint = {1904.05551},
 primaryClass = {math.GR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190405551B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@book {fgcm,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A.},
     TITLE = {Finitely generated commutative monoids},
 PUBLISHER = {Nova Science Publishers, Inc., Commack, NY},
      YEAR = {1999},
     PAGES = {xiv+185},
      ISBN = {1-56072-670-9},
   MRCLASS = {20M14},
  MRNUMBER = {1694173},
}


@book {nsapp,
    AUTHOR = {Assi, Abdallah and Garc\'{\i}a-S\'{a}nchez, Pedro A.},
     TITLE = {Numerical semigroups and applications},
    SERIES = {RSME Springer Series},
    VOLUME = {1},
 PUBLISHER = {Springer, [Cham]},
      YEAR = {2016},
     PAGES = {xiv+106},
      ISBN = {978-3-319-41329-7; 978-3-319-41330-3},
   MRCLASS = {20M14 (14G50 14H50 68W30)},
  MRNUMBER = {3558713},
       DOI = {10.1007/978-3-319-41330-3},
       URL = {https://doi.org/10.1007/978-3-319-41330-3},
}

@article {R07,
    AUTHOR = {Rosales, J. C.},
     TITLE = {Subadditive periodic functions and numerical semigroups},
   JOURNAL = {J. Algebra Appl.},
  FJOURNAL = {Journal of Algebra and its Applications},
    VOLUME = {6},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {305--313},
      ISSN = {0219-4988},
   MRCLASS = {20M14},
  MRNUMBER = {2316425},
MRREVIEWER = {Attila Nagy},
       DOI = {10.1142/S0219498807002223},
       URL = {https://doi.org/10.1142/S0219498807002223},
}

@article {RGSGGJM,
    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},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {189},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {301--313},
      ISSN = {0022-4049},
   MRCLASS = {20M14},
  MRNUMBER = {2038577},
       DOI = {10.1016/j.jpaa.2003.10.024},
       URL = {https://doi.org/10.1016/j.jpaa.2003.10.024},
}

@article {RGSUB,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A. and Urbano-Blanco, J.
              M.},
     TITLE = {Modular {D}iophantine inequalities and numerical semigroups},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {218},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {379--398},
      ISSN = {0030-8730},
   MRCLASS = {20M14 (20M05 20M30)},
  MRNUMBER = {2218353},
MRREVIEWER = {Muhammad Zafrullah},
       DOI = {10.2140/pjm.2005.218.379},
       URL = {https://doi.org/10.2140/pjm.2005.218.379},
}

@article {RUB,
    AUTHOR = {Rosales, J. C. and Urbano-Blanco, J. M.},
     TITLE = {Opened modular numerical semigroups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {306},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {368--377},
      ISSN = {0021-8693},
   MRCLASS = {20M10},
  MRNUMBER = {2271340},
MRREVIEWER = {Inessa Levi},
       DOI = {10.1016/j.jalgebra.2006.08.009},
       URL = {https://doi.org/10.1016/j.jalgebra.2006.08.009},
}

@article {RosalesVasco2008MIA,
    AUTHOR = {Rosales, J. C. and Vasco, P.},
     TITLE = {The smallest positive integer that is solution of a
              proportionally modular {D}iophantine inequality},
   JOURNAL = {Math. Inequal. Appl.},
  FJOURNAL = {Mathematical Inequalities \& Applications},
    VOLUME = {11},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {203--212},
      ISSN = {1331-4343},
   MRCLASS = {20M14 (11D75)},
  MRNUMBER = {2410272},
MRREVIEWER = {P. G. Trotter},
       DOI = {10.7153/mia-11-14},
       URL = {https://doi.org/10.7153/mia-11-14},
}