  
  
  [1XReferences[101X
  
  [[20X4t[120X]  [16X4ti2  team,  [116X,  [17X4ti2---A software package for algebraic, geometric and
  combinatorial problems on linear spaces[117X, {A}vailable at www.4ti2.de.
  
  [[20XAG10[120X]  [16XAguil{\'o}-Gost,  F. and Garc{\'{\i}}a-S{\'a}nchez, P. A.[116X, [17XFactoring
  in embedding dimension three numerical semigroups[117X, [18XElectron. J. Combin.[118X, [19X17[119X,
  1 (2010), Research Paper 138, 21.
  
  [[20XAG13[120X]  [16XAssi,  A.  and Garc\'{\i}a-S\'anchez, P. A.[116X, [17XConstructing the set of
  complete  intersection  numerical  semigroups with a given Frobenius number[117X,
  [18XApplicable Algebra in Engineering, Communication and Computing[118X (2013).
  
  [[20XAG14[120X]  [16XAssi,  A. and Garc\'{\i}a-S\'anchez, P. A.[116X, [17XOn curves with one place
  at infinity[117X, [18XarXiv[118X, [19X1407.0490[119X (2014).
  
  [[20XAGM14[120X]  [16XAssi,  A.,  Garc\'{\i}a-S\'anchez,  P.  A. and Micale, V.[116X, [17XBases of
  subalgebras of K[[x]] and K[x][117X, [18XarXiv[118X, [19X1412.4089[119X (2014).
  
  [[20XBGJLLM14[120X]  [16XBarakat,  M.,  Gutsche,  S.,  Jambor,  S.,  Lange-Hegermann, M.,
  Lorenz,  A.  and  Motsak,  O.[116X, [17XGradedModules, A homalg based package for the
  Abelian category of finitely presented graded modules over computable graded
  rings,     Version     2014.09.17[117X    (2014),    ((GAP    package)),    \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/}}.
  
  [[20XBOP14[120X]  [16XBarron, T., O'Neill, C. and Pelayo, R.[116X, [17XOn the computation of delta
  sets and ω-primality in numerical monoids[117X, [18Xpreprint[118X (2014).
  
  [[20XBDF97[120X]  [16XBarucci, V., Dobbs, D. D. and Fontana, M.[116X, [17XMaximality properties in
  numerical   semigroups  and  applications  to  one-dimensional  analytically
  irreducible  local  domains[117X,  American  Mathematical Society, Memoirs of the
  American Mathematical Society, 598 (1997).
  
  [[20XBF06[120X]   [16XBarucci,   V.   and  Fr\"oberg,  R.[116X,  [17XAssociated  graded  rings  of
  one-dimensional  analytically  irreducible  rings[117X,  [18XJ.  Algebra[118X, [19X304[119X (2006),
  349--358.
  
  [[20XBR97[120X]  [16XBarucci,  V. and R., F.[116X, [17XOne-dimensional almost Gorenstein Rings[117X, [18XJ.
  Algebra[118X, [19X188[119X (1997), 418--442.
  
  [[20XBC77[120X]  [16XBertin,  J.  and Carbonne, P.[116X, [17XSemi-groupes d'entiers et application
  aux branches[117X, [18XJ. Algebra[118X, [19X49[119X, 1 (1977), 81--95.
  
  [[20XBGG11[120X]  [16XBlanco,  V.,  Garc\'{\i}a-S\'anchez,  P.  A.  and  Geroldinger, A.[116X,
  [17XSemigroup-theoretical  characterizations  of  arithmetical  invariants  with
  applications  to  numerical monoids and Krull monoids[117X, [18XIllinois J. Math.[118X, [19X55[119X
  (2011), 1385--1414.
  
  [[20XBR13[120X]  [16XBlanco,  V.  and  Rosales,  J. C.[116X, [17XThe tree of irreducible numerical
  semigroups   with  fixed  Frobenius  number[117X,  [18XForum  Math.[118X,  [19X25[119X,  6  (2013),
  1249--1261.
  
  [[20XBD89[120X]  [16XBradford, R. J. and Davenport, J. H.[116X, [17XEffective tests for cyclotomic
  polynomials[117X,  in  Symbolic and algebraic computation (Rome, 1988), Springer,
  Berlin, Lecture Notes in Comput. Sci., [19X358[119X (1989), 244--251.
  
  [[20XBra08[120X]   [16XBras-Amor\'os,  M.[116X,  [17XFibonacci-like  behavior  of  the  number  of
  numerical semigroups of a given genus[117X, [18XSemigroup Forum[118X, [19X76[119X (2008), 379--384.
  
  [[20XBIRC14[120X]  [16XBruns, W., Ichim, B., R\"omer, T. and C., S.[116X, [17XNormaliz. Algorithms
  for       rational      cones      and      affine      monoids[117X      (2014),
  \url{http://www.math.uos.de/normaliz}.
  
  [[20XBry10[120X]  [16XBryant,  L.[116X,  [17XGoto  numbers  of  a numerical semigroup ring and the
  Gorensteiness  of  associated  graded  rings[117X,  [18XComm.  Algebra[118X, [19X38[119X, 6 (2010),
  2092--2128.
  
  [[20XBH13[120X]  [16XBryant,  L.  and  Hamblin, J.[116X, [17XThe maximal denumerant of a numerical
  semigroup[117X, [18XSemigroup Forum[118X, [19X86[119X, 3 (2013), 571--582.
  
  [[20XBR09[120X]  [16XBullejos,  M. and Rosales, J. C.[116X, [17XProportionally modular Diophantine
  inequalities  and  the  Stern-Brocot  tree[117X,  [18XMath.  Comp.[118X,  [19X78[119X,  266 (2009),
  1211--1226.
  
  [[20XCGB02[120X]  [16XC.,  R., Garc\'{\i}a-S\'anchezP. A. and Garc\'{\i}a-Garc\'{\i}a, J.
  I.  and  Branco,  M.  B.[116X,  [17XSYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS[117X,
  [18XJournal of the London Mathematical Society[118X, [19X65[119X (2002), 611--623.
  
  [[20XCGD07[120X]  [16XChapman,  S.  T.,  Garc\'{\i}a-S\'anchez,  P.  A.  and  D., L.[116X, [17XThe
  catenary and tame degree of numerical semigroups[117X, [18XForum Math.[118X (2007), 1--13.
  
  [[20XCGLPR06[120X]   [16XChapman,   S.  T.,  Garc\'{\i}a-S\'anchez,  P.  A.,  Llena,  D.,
  Ponomarenko, V. and Rosales, J. C.[116X, [17XThe catenary and tame degree in finitely
  generated  commutative  cancellative  monoids[117X,  [18XManuscripta  Math.[118X,  [19X120[119X,  3
  (2006), 253--264.
  
  [[20XCHM06[120X]  [16XChapman,  S. T., Holden, M. T. and Moore, T. A.[116X, [17XFull elasticity in
  atomic  monoids and integral domains[117X, [18XRocky Mountain J. Math.[118X, [19X36[119X, 5 (2006),
  1437--1455.
  
  [[20XCA13[120X]  [16XChappelon,  J.  and  Ram{\'{\i}}rez  Alfons{\'{\i}}n,  J. L.[116X, [17XOn the
  M\"obius  function  of  the locally finite poset associated with a numerical
  semigroup[117X, [18XSemigroup Forum[118X, [19X87[119X, 2 (2013), 313--330.
  
  [[20XCD94[120X]  [16XContejean,  E. and Devie, H.[116X, [17XAn efficient incremental algorithm for
  solving systems of linear Diophantine equations[117X, [18XInform. and Comput.[118X, [19X113[119X, 1
  (1994), 143--172.
  
  [[20XBJA13[120X]  [16XCortadellas Ben\'{\i}tez, T., Jafari, R. and Zarzuela Armengou, S.[116X,
  [17XOn  teh  Ap\'ery  sets  of  monomial  curves[117X,  [18XSemigroup  Forum[118X,  [19X86[119X (2013),
  289--320.
  
  [[20XCG12[120X]  [16XCostantini,  M.  and  de  Graaf,  W.[116X,  [17XGAP package singular; the GAP
  interface                 to                 Singular[117X                (2012),
  \url{http://gap-system.org/Packages/singular.html}.
  
  [[20XDMV09[120X]  [16XD'Anna,  M., Mezzasalma, M. and V., M.[116X, [17XOn the Buchsbaumness of the
  associated  graded  ring  of a one-dimensional local ring[117X, [18XComm. Algebra[118X, [19X37[119X
  (2009), 1594--1603.
  
  [[20XDMS11[120X]  [16XD'Anna, M., Micale, V. and Sammartano, A.[116X, [17XOn the associated graded
  ring of a semigroup ring[117X, [18XJ. Commut. Algebra[118X, [19X3[119X, 2 (2011), 147--168.
  
  [[20XDMS13[120X]  [16XD'Anna,  M.,  Micale,  V.  and  Sammartano, A.[116X, [17XWhen the associated
  graded  ring  of  a  semigroup  ring is complete intersection[117X, [18XJ. Pure Appl.
  Algebra[118X, [19X217[119X, 6 (2013), 1007--1017.
  
  [[20XDMS14[120X]  [16XD'Anna,  M.,  Micale,  V.  and  Sammartano, A.[116X, [17XClasses of complete
  intersection numerical semigroups[117X, [18XSemigroup Forum[118X, [19X88[119X, 2 (2014), 453--467.
  
  [[20XDGPS12[120X]  [16XDecker,  W.,  Greuel, G.-M., Pfister, G. and Sch\"onemann, H.[116X, [17X\sc
  Singular  3-1-6  ---  A  computer algebra system for polynomial computations[117X
  (2012), \url{http://www.singular.uni-kl.de}.
  
  [[20XDGM06[120X] [16XDelgado, M., Garc\'{\i}a-S\'anchez, P. A. and Morais, J.[116X, [17XOn the GAP
  package  numericalsgps[117X,  in  Fifth  Conference  on  Discrete Mathematics and
  Computer  Science  (Spanish),  Univ.  Valladolid, Ciencias (Valladolid), [19X23[119X,
  Secr. Publ. Intercamb. Ed., Valladolid (2006), 271--278.
  
  [[20XES96[120X] [16XEisenbud, D. and Sturmfels, B.[116X, [17XBinomial ideals[117X, [18XDuke Math. J.[118X, [19X84[119X, 1
  (1996), 1--45.
  
  [[20XEli01[120X]  [16XElias,  J.[116X,  [17XOn  the  deep  structure  of  the  blowing-up of curve
  singularities[117X, [18XMath. Proc. Camb. Phil. Soc.[118X, [19X131[119X (2001), 227--240.
  
  [[20XFGR87[120X]  [16XFr\"oberg,  R.,  Gottlieb,  C. and R., H.[116X, [17XOn numerical semigroups[117X,
  [18XSemigroup Forum[118X, [19X35[119X, 1 (1987), 63--83.
  
  [[20XGMV14[120X]   [16XGarc\'{\i}a-Garc\'{\i}a,  J.  I.,  Moreno-Fr\'{\i}as,  M.  A.  and
  Vigneron-Tenorio,  A.[116X,  [17XComputation  of  Delta  sets  of  numerical monoids[117X,
  [18Xarxiv:1406.0280[118X (2014).
  
  [[20XGar14[120X]  [16XGarc\'{\i}a-S\'anchez, P. A.[116X, [17XA new approach for the computation of
  the tame degree[117X, [18Xarxiv:1504.02998[118X (2014).
  
  [[20XGO10[120X]  [16XGarc\'{\i}a-S\'anchez,  P.  A.  and  Ojeda,  I.[116X,  [17XUniquely presented
  finitely  generated  commutative  monoids[117X,  [18XPacific  J.  Math.[118X,  [19X249[119X (2010),
  91--105.
  
  [[20XSO-13[120X]  [16XGarc{\'{\i}}a  S{\'a}nchez,  P.  A.,  Ojeda,  I. and S{\'a}nchez-R.
  -Navarro,  A.[116X, [17XFactorization invariants in half-factorial affine semigroups[117X,
  [18XInternat. J. Algebra Comput.[118X, [19X23[119X, 1 (2013), 111--122.
  
  [[20XGH06[120X]  [16XGeroldinger,  A.  and  Halter-Koch,  F.[116X,  [17XNon-unique Factorizations:
  Algebraic, Combinatorial and Analytic Theory[117X, Chapman \& Hall/CRC (2006).
  
  [[20XGut[120X]     [16XGutsche,     S.[116X,     [17X4ti2Interface,     A     link     to    4ti2[117X,
  \url{http://www.gap-system.org/Packages/4ti2interface.html}.
  
  [[20XGHS14[120X]  [16XGutsche,  S.,  Horn,  M. and S\"oger, C.[116X, [17XNormalizInterface for GAP[117X
  (2014), \url{https://github.com/fingolfin/NormalizInterface}.
  
  [[20XHS04[120X]  [16XHerzinger,  K. and Sanford, R.[116X, [17XMinimal Generating Sets for Relative
  Ideals  in  Numerical  Semigroups  of  Multiplicity Eight[117X, [18XCommunications in
  Algebra[118X, [19X32[119X, 12 (2004), 4713-4731.
  
  [[20XHer70[120X]  [16XHerzog,  J.[116X,  [17XGenerators  and  relations  of abelian semigroups and
  semigroup rings. [117X, [18XManuscripta Math.[118X, [19X3[119X (1970), 175--193.
  
  [[20XKP95[120X]  [16XKirfel,  C.  and  Pellikaan, R.[116X, [17XThe minimum distance of codes in an
  array  coming from telescopic semigroups[117X, [18XIEEE Trans. Inform. Theory[118X, [19X41[119X, 6,
  part 1 (1995), 1720--1732, ((Special issue on algebraic geometry codes)).
  
  [[20XMic02[120X]  [16XMicale,  V.[116X,  [17XOn monomial semigroups[117X, [18XCommunications in Algebra[118X, [19X30[119X
  (2002), 4687 - 4698.
  
  [[20XMor14[120X]   [16XMoree,  P.[116X,  [17XNumerical  semigroups,  cyclotomic  polynomials,  and
  Bernoulli numbers[117X, [18XAmer. Math. Monthly[118X, [19X121[119X, 10 (2014), 890--902.
  
  [[20XPhi10[120X]  [16XPhilipp,  A.[116X,  [17XA characterization of arithmetical invariants by the
  monoid of relations[117X, [18XSemigroup Forum[118X, [19X81[119X (2010), 424--434.
  
  [[20XRos96a[120X] [16XRosales, J. C.[116X, [17XAn algorithmic method to compute a minimal relation
  for  any  numerical  semigroup[117X,  [18XInternat.  J.  Algebra  Comput.[118X,  [19X6[119X (1996),
  441-455.
  
  [[20XRos96b[120X]  [16XRosales,  J.  C.[116X,  [17XOn  numerical  semigroups[117X,  [18XSemigroup Forum[118X, [19X52[119X
  (1996), 307-318.
  
  [[20XRB03[120X]  [16XRosales,  J. C. and Branco, M. B.[116X, [17XIrreducible numerical semigroups[117X,
  [18XPacific J. Math.[118X, [19X209[119X, 1 (2003), 131--143.
  
  [[20XRG98[120X] [16XRosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.[116X, [17XNonnegative elements
  of  subgroups  of \(\mathbbZ^n\)[117X, [18XLinear Algebra and its Applications [118X, [19X270[119X,
  1-3 (1998), 351- 357, (()).
  
  [[20XRG99a[120X]  [16XRosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.[116X, [17XFinitely generated
  commutative monoids[117X, Nova Science Publishers, New York (1999).
  
  [[20XRG04[120X]  [16XRosales,  J.  C.  and  Garc\'{\i}a-S\'anchez,  P. A.[116X, [17XEvery positive
  integer  is  the Frobenius number of an irreducible numerical semigroup with
  at most four generators[117X, [18XArk. Mat.[118X, [19X42[119X (2004), 301-306.
  
  [[20XRG09[120X]   [16XRosales,   J.   C.  and  Garc\'{\i}a-S\'anchez,  P.  A.[116X,  [17XNumerical
  Semigroups[117X, Springer (2009).
  
  [[20XRGGB03[120X]     [16XRosales,     J.     C.,     Garc\'{\i}a-S\'anchez,    P.    A.,
  Garc\'{\i}a-Garc\'{\i}a,  J. I. and Branco, M. B.[116X, [17XNumerical semigroups with
  maximal embedding dimension[117X, [18XJ. Algebra[118X, [19X2[119X (2003), 47--53.
  
  [[20XRGGB04[120X]     [16XRosales,     J.     C.,     Garc\'{\i}a-S\'anchez,    P.    A.,
  Garc\'{\i}a-Garc\'{\i}a,  J. I. and Branco, M. B.[116X, [17XArf numerical semigroups[117X,
  [18XJ. Algebra[118X, [19X276[119X (2004), 3--12.
  
  [[20XRGGM04[120X]     [16XRosales,     J.     C.,     Garc\'{\i}a-S\'anchez,    P.    A.,
  Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'enez Madrid, J. A.[116X, [17XFundamental gaps
  in numerical semigroups[117X, [18XJ. Pure Appl. Algebra[118X, [19X189[119X, 1-3 (2004), 301--313.
  
  [[20XRGGJ03[120X]     [16XRosales,     J.     C.,     Garc\'{\i}a-S\'anchez,    P.    A.,
  Garc\'{\i}a-Garc\'{\i}a,   J.   I.   and   Jim\'enez-Madrid,   J.   A.[116X,  [17XThe
  oversemigroups  of  a  numerical  semigroup[117X,  [18XSemigroup  Forum[118X,  [19X67[119X  (2003),
  145-158.
  
  [[20XRG13[120X]  [16XRosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.[116X, [17XConstructing almost
  symmetric numerical semigroups from almost irreducible numerical semigroups[117X,
  [18XComm. Algebra[118X (to appear 2013).
  
  [[20XRG99b[120X]  [16XRosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.[116X, [17XOn free affine
  semigroups[117X, [18XSemigroup Forum[118X, [19X58[119X, 3 (1999), 367--385.
  
  [[20XSpi14[120X]  [16XSpirito, D.[116X, [17XStar operations on numerical semigroups[117X, [18XComm. Algebra[118X
  (to appear 2014).
  
  [[20XSW86[120X]  [16XSz{\'e}kely,  L. A. and Wormald, N. C.[116X, [17XGenerating functions for the
  Frobenius  problem  with  2  and  3  generators[117X, [18XMath. Chronicle[118X, [19X15[119X (1986),
  49--57.
  
  [[20XZar86[120X]  [16XZariski,  O.[116X,  [17XLe  probl\`eme  des modules pour les courbes planes[117X,
  Hermann (1986).
  
  [[20X{{{15[120X]    [16X{Delgado},    M.,    {Garc{\'{\i}}a-S{\'a}nchez},   P.   A.   and
  {Robles-P{\'e}rez},  A.  M.[116X,  [17XNumerical  semigroups  with  a  given  set  of
  pseudo-Frobenius numbers[117X, [18XArXiv e-prints[118X (2015).
  
  
  
  [32X
