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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346@incollection {JMDA,1AUTHOR = {Delgado, M. and Garc\'{\i}a-S\'anchez, P. A. and Morais, J.},2TITLE = {On the {GAP} package numericalsgps},3BOOKTITLE = {Fifth {C}onference on {D}iscrete {M}athematics and {C}omputer4{S}cience ({S}panish)},5SERIES = {Ciencias (Valladolid)},6VOLUME = {23},7PAGES = {271--278},8PUBLISHER = {Univ. Valladolid},9ADDRESS = {Secr. Publ. Intercamb. 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T. and Garc\'{\i}a-S\'anchez, P. A. and Llena, D. and Ponomarenko, V. and Rosales, J. C.",192title = {The catenary and tame degree in finitely generated commutative cancellative193monoids},194journal = {Manuscripta Math.},195year = {2006},196volume = {120},197pages = {253--264},198number = {3}199}200201@Article{CGL,202author= "Chapman, S. T. and Garc\'{\i}a-S\'anchez, P. A. and Llena D.",203title= "The catenary and tame degree of numerical semigroups",204journal = {Forum Math.},205year = {2007},206pages = {1--13}207}208209210@Article{CHM06,211author= "Chapman, S. T. and Holden, M. T. and Moore, T. A.",212title= "Full elasticity in atomic monoids and integral domains",213journal= {Rocky Mountain J. Math.},214Volume = {36},215Number ={5},216year = 2006,217Pages = {1437--1455}218}219220221@Article{BF06,222author= {Barucci, V. and Fr\"oberg, R.},223title= "Associated graded rings of one-dimensional analytically224irreducible rings",225journal= "J. Algebra",226volume= "304",227year= "2006",228pages = "349--358"229}230231232@Article{E01,233author= "Elias, J.",234title= "On the deep structure of the blowing-up of curve singularities",235journal= "Math. Proc. Camb. Phil. Soc.",236volume= "131",237year= "2001",238pages= "227--240"239}240241242@Article{B06,243author= "Barucci, V.",244title= "Numerical semiroup algebras",245journal= "Multiplicative Ideal Theory in Commutative Algebra,246a tribute to the work of Robert Gilmer",247publisher= "Springer Science and Business Media",248year="2006"249}250251@ARTICLE{VMic02,252author = {Micale, V.},253title = {On monomial semigroups},254journal = {Communications in Algebra},255year = {2002},256volume = {30},257pages = {4687 - 4698}258}259@ARTICLE{B-A08,260author = {Bras-Amor\'os, M.},261title = {Fibonacci-like behavior of the number of numerical semigroups of262a given genus},263journal = {Semigroup Forum},264year = {2008},265volume = {76},266pages = {379--384}267}268269@article {BA-GS,270AUTHOR = {Bras-Amor{\'o}s, Maria and Garc{\'{\i}}a-S{\'a}nchez, Pedro271A.},272TITLE = {Patterns on numerical semigroups},273JOURNAL = {Linear Algebra Appl.},274FJOURNAL = {Linear Algebra and its Applications},275VOLUME = {414},276YEAR = {2006},277NUMBER = {2-3},278PAGES = {652--669},279ISSN = {0024-3795},280CODEN = {LAAPAW},281MRCLASS = {20M14},282MRNUMBER = {2214415 (2007b:20129)},283MRREVIEWER = {Andrei Kelarev},284DOI = {10.1016/j.laa.2005.11.007},285URL = {http://dx.doi.org/10.1016/j.laa.2005.11.007},286}287288289@Article{GS-O,290author= "Garc\'{\i}a-S\'anchez, P. A. and Ojeda, I.",291title= "Uniquely presented finitely generated commutative monoids",292journal= "Pacific J. Math.",293volume= "249",294year= "2010",295pages = "91--105"296}297298@Article{B-GS-G,299author= "Blanco, V. and Garc\'{\i}a-S\'anchez, P. A. and Geroldinger, A",300title= "Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids",301journal= "Illinois J. Math.",302volume= "55",303year= "2011",304pages = "1385--1414"305}306307@Article{DA-M-M,308author= "D'Anna, M. and Mezzasalma, M. and Micale V.",309title="On the Buchsbaumness of the associated graded ring of a one-dimensional local ring",310journal="Comm. Algebra",311volume="37",312year= "2009",313pages="1594--1603"314}315316@article {DA-M-S,317AUTHOR = {D'Anna, M. and Micale, V. and Sammartano, A.},318TITLE = {On the associated graded ring of a semigroup ring},319JOURNAL = {J. Commut. Algebra},320FJOURNAL = {Journal of Commutative Algebra},321VOLUME = {3},322YEAR = {2011},323NUMBER = {2},324PAGES = {147--168},325ISSN = {1939-0807},326MRCLASS = {13A30 (13H10)},327MRNUMBER = {2813470},328}329330331@Article {Br,332AUTHOR = {Bryant, L.},333TITLE = {Goto numbers of a numerical semigroup ring and the334{G}orensteiness of associated graded rings},335JOURNAL = {Comm. Algebra},336FJOURNAL = {Communications in Algebra},337VOLUME = {38},338YEAR = {2010},339NUMBER = {6},340PAGES = {2092--2128},341ISSN = {0092-7872},342CODEN = {COALDM},343MRCLASS = {20M25 (13A30 13C40 20M14)},344MRNUMBER = {2675524},345MRREVIEWER = {Grigori I. {\v{Z}}itomirski{\u\i}},346DOI = {10.1080/00927870903025993},347URL = {http://dx.doi.org/10.1080/00927870903025993},348}349350@Article{BR13,351AUTHOR = {Blanco, Victor and Rosales, Jos{\'e} Carlos},352TITLE = {The tree of irreducible numerical semigroups with fixed353{F}robenius number},354JOURNAL = {Forum Math.},355FJOURNAL = {Forum Mathematicum},356VOLUME = {25},357YEAR = {2013},358NUMBER = {6},359PAGES = {1249--1261},360ISSN = {0933-7741},361MRCLASS = {11D07 (05A18 13H10 20M14)},362MRNUMBER = {3199729},363MRREVIEWER = {Raheleh Jafari},364DOI = {10.1515/form.2011.151},365URL = {http://dx.doi.org/10.1515/form.2011.151},366}367368@article {MR3169635,369AUTHOR = {Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},370TITLE = {Constructing almost symmetric numerical semigroups from371irreducible numerical semigroups},372JOURNAL = {Comm. Algebra},373FJOURNAL = {Communications in Algebra},374VOLUME = {42},375YEAR = {2014},376NUMBER = {3},377PAGES = {1362--1367},378ISSN = {0092-7872},379MRCLASS = {20M14 (20M25)},380MRNUMBER = {3169635},381MRREVIEWER = {Attila Nagy},382DOI = {10.1080/00927872.2012.740117},383URL = {http://dx.doi.org/10.1080/00927872.2012.740117},384}385386@article {MR3354072,387AUTHOR = {Spirito, Dario},388TITLE = {Star operations on numerical semigroups},389JOURNAL = {Comm. Algebra},390FJOURNAL = {Communications in Algebra},391VOLUME = {43},392YEAR = {2015},393NUMBER = {7},394PAGES = {2943--2963},395ISSN = {0092-7872},396MRCLASS = {20M14 (13A99)},397MRNUMBER = {3354072},398DOI = {10.1080/00927872.2014.908201},399URL = {http://dx.doi.org/10.1080/00927872.2014.908201},400}401402@Article{BF97,403author={Barucci, V. and Fr\"oberg R.},404title={One-dimensional almost Gorenstein Rings},405journal={J. Algebra},406volume={188},407year={1997},408pages={418--442}409}410411@article {BC77,412AUTHOR = {Bertin, J. and Carbonne, P.},413TITLE = {Semi-groupes d'entiers et application aux branches},414JOURNAL = {J. Algebra},415FJOURNAL = {Journal of Algebra},416VOLUME = {49},417YEAR = {1977},418NUMBER = {1},419PAGES = {81--95},420ISSN = {0021-8693},421MRCLASS = {14B05},422MRNUMBER = {0568894 (58 \#27957)},423}424425@article {KP95,426AUTHOR = {Kirfel, Christoph and Pellikaan, Ruud},427TITLE = {The minimum distance of codes in an array coming from428telescopic semigroups},429NOTE = {Special issue on algebraic geometry codes},430JOURNAL = {IEEE Trans. Inform. Theory},431FJOURNAL = {Institute of Electrical and Electronics Engineers.432Transactions on Information Theory},433VOLUME = {41},434YEAR = {1995},435NUMBER = {6, part 1},436PAGES = {1720--1732},437ISSN = {0018-9448},438CODEN = {IETTAW},439MRCLASS = {94B27 (94B35)},440MRNUMBER = {1391031 (97e:94015)},441DOI = {10.1109/18.476245},442URL = {http://dx.doi.org/10.1109/18.476245},443}444445@article{AGS13,446author={Assi, A. and Garc\'{\i}a-S\'anchez, P. A.},447title={Constructing the set of complete intersection numerical semigroups with a given Frobenius number},448journal={Applicable Algebra in Engineering, Communication and Computing},449year={2013}450}451452@article{AGS14,453author={Assi, A. and Garc\'{\i}a-S\'anchez, P. A.},454title={Algorithms for curves with one place at infinity},455journal= "Journal of Symbolic Computation",456volume= "74",457pages= "475--492",458year= "2016"459}460461@article{AGSM14,462author={Assi, A. and Garc\'{\i}a-S\'anchez, P. A. and V. Micale},463title={Bases of subalgebras of K[[x]] and K[x]},464journal= "Journal of Symbolic Computation",465volume= "79",466pages= " 4--22",467year= "2017"468}469470@book{Z86,471author={Zariski, O.},472title={Le probl\`eme des modules pour les courbes planes},473year={1986},474publisher={Hermann}475}476477@BOOK{RGbook,478title = {Numerical Semigroups},479publisher = {Springer},480year = {2009},481author = {Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.}482}483484@article{DAMSwhen,485AUTHOR = {D'Anna, M. and Micale, V. and Sammartano, A.},486TITLE = {When the associated graded ring of a semigroup ring is487complete intersection},488JOURNAL = {J. Pure Appl. Algebra},489FJOURNAL = {Journal of Pure and Applied Algebra},490VOLUME = {217},491YEAR = {2013},492NUMBER = {6},493PAGES = {1007--1017},494ISSN = {0022-4049},495CODEN = {JPAAA2},496MRCLASS = {13A30 (13C40 14M10)},497MRNUMBER = {3010100},498MRREVIEWER = {Zhongming Tang},499DOI = {10.1016/j.jpaa.2012.09.024},500URL = {http://dx.doi.org/10.1016/j.jpaa.2012.09.024},501}502@article{DAMSClasses,503AUTHOR = {D'Anna, Marco and Micale, Vincenzo and Sammartano, Alessio},504TITLE = {Classes of complete intersection numerical semigroups},505JOURNAL = {Semigroup Forum},506FJOURNAL = {Semigroup Forum},507VOLUME = {88},508YEAR = {2014},509NUMBER = {2},510PAGES = {453--467},511ISSN = {0037-1912},512MRCLASS = {20M14},513MRNUMBER = {3189106},514MRREVIEWER = {M. A. Moreno-Fr{\'{\i}}as},515DOI = {10.1007/s00233-013-9547-y},516URL = {http://dx.doi.org/10.1007/s00233-013-9547-y},517}518519@article{CJZ,520author={Cortadellas Ben\'{\i}tez, T. and Jafari, R. and Zarzuela Armengou, S.},521title={On teh Ap\'ery sets of monomial curves},522journal={Semigroup Forum},523year={2013},524volume={86},525pages={289--320},526doi={DOI 10.1007/s00233-012-9445-8}527}528529@article{PH,530author={Philipp, A.},531title={A characterization of arithmetical invariants by the monoid of relations},532journal={Semigroup Forum},533volume={81},534year={2010},535pages={424--434}536}537538@article {BH,539AUTHOR = {Bryant, Lance and Hamblin, James},540TITLE = {The maximal denumerant of a numerical semigroup},541JOURNAL = {Semigroup Forum},542FJOURNAL = {Semigroup Forum},543VOLUME = {86},544YEAR = {2013},545NUMBER = {3},546PAGES = {571--582},547ISSN = {0037-1912},548CODEN = {SMGFAN},549MRCLASS = {20M14},550MRNUMBER = {3053780},551DOI = {10.1007/s00233-012-9448-5},552URL = {http://dx.doi.org/10.1007/s00233-012-9448-5},553}554555@article {GSOSN,556AUTHOR = {Garc{\'{\i}}a S{\'a}nchez, P. A. and Ojeda, I. and557S{\'a}nchez-R.-Navarro, A.},558TITLE = {Factorization invariants in half-factorial affine semigroups},559JOURNAL = {Internat. J. Algebra Comput.},560FJOURNAL = {International Journal of Algebra and Computation},561VOLUME = {23},562YEAR = {2013},563NUMBER = {1},564PAGES = {111--122},565ISSN = {0218-1967},566MRCLASS = {20M14 (20M13)},567MRNUMBER = {3040805},568DOI = {10.1142/S0218196713500033},569URL = {http://dx.doi.org/10.1142/S0218196713500033},570}571572@book {CLOS,573AUTHOR = {Cox, David and Little, John and O'Shea, Donal},574TITLE = {Ideals, varieties, and algorithms},575SERIES = {Undergraduate Texts in Mathematics},576EDITION = {Third},577NOTE = {An introduction to computational algebraic geometry and578commutative algebra},579PUBLISHER = {Springer},580ADDRESS = {New York},581YEAR = {2007},582PAGES = {xvi+551},583ISBN = {978-0-387-35650-1; 0-387-35650-9},584MRCLASS = {13P10 (13-01 14-01 14Qxx 68W30)},585MRNUMBER = {2290010 (2007h:13036)},586DOI = {10.1007/978-0-387-35651-8},587URL = {http://dx.doi.org/10.1007/978-0-387-35651-8},588}589590591@article {CHRA,592AUTHOR = {Chappelon, Jonathan and Ram{\'{\i}}rez Alfons{\'{\i}}n, Jorge593Luis},594TITLE = {On the {M}\"obius function of the locally finite poset595associated with a numerical semigroup},596JOURNAL = {Semigroup Forum},597FJOURNAL = {Semigroup Forum},598VOLUME = {87},599YEAR = {2013},600NUMBER = {2},601PAGES = {313--330},602ISSN = {0037-1912},603MRCLASS = {06F05 (05E05 06A06 20M14)},604MRNUMBER = {3110597},605MRREVIEWER = {V{\'a}clav Koubek},606DOI = {10.1007/s00233-012-9458-3},607URL = {http://dx.doi.org/10.1007/s00233-012-9458-3},608}609610@incollection {BD-cyclotomic,611AUTHOR = {Bradford, R. J. and Davenport, J. H.},612TITLE = {Effective tests for cyclotomic polynomials},613BOOKTITLE = {Symbolic and algebraic computation ({R}ome, 1988)},614SERIES = {Lecture Notes in Comput. Sci.},615VOLUME = {358},616PAGES = {244--251},617PUBLISHER = {Springer, Berlin},618YEAR = {1989},619MRCLASS = {11Y16 (11Y40)},620MRNUMBER = {1034734 (90m:11201)},621MRREVIEWER = {Lajos R{\'o}nyai},622DOI = {10.1007/3-540-51084-2_22},623URL = {http://dx.doi.org/10.1007/3-540-51084-2_22},624}625626@Article{M,627AUTHOR = {Moree, Pieter},628TITLE = {Numerical semigroups, cyclotomic polynomials, and {B}ernoulli629numbers},630JOURNAL = {Amer. Math. Monthly},631FJOURNAL = {American Mathematical Monthly},632VOLUME = {121},633YEAR = {2014},634NUMBER = {10},635PAGES = {890--902},636ISSN = {0002-9890},637MRCLASS = {11B68 (11C08)},638MRNUMBER = {3295662},639DOI = {10.4169/amer.math.monthly.121.10.890},640URL = {http://dx.doi.org/10.4169/amer.math.monthly.121.10.890},641}642643644@article{SzW,645AUTHOR = {Sz{\'e}kely, L. A. and Wormald, N. C.},646TITLE = {Generating functions for the {F}robenius problem with {$2$}647and {$3$} generators},648JOURNAL = {Math. Chronicle},649FJOURNAL = {Mathematical Chronicle},650VOLUME = {15},651YEAR = {1986},652PAGES = {49--57},653ISSN = {0581-1155},654CODEN = {MTHCB3},655MRCLASS = {05A15 (11D04 11P99)},656MRNUMBER = {900339 (88i:05013)},657MRREVIEWER = {Volker Strehl},658}659660@article{AG-GS,661AUTHOR = {Aguil{\'o}-Gost, F. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},662TITLE = {Factoring in embedding dimension three numerical semigroups},663JOURNAL = {Electron. J. Combin.},664FJOURNAL = {Electronic Journal of Combinatorics},665VOLUME = {17},666YEAR = {2010},667NUMBER = {1},668PAGES = {Research Paper 138, 21},669ISSN = {1077-8926},670MRCLASS = {11D07 (05B45 05C90 11D45)},671MRNUMBER = {2729387 (2011j:11050)},672MRREVIEWER = {Lajos Hajdu},673URL =674{http://www.combinatorics.org/Volume_17/Abstracts/v17i1r138.html},675}676677@article{B-P-ON,678AUTHOR = {Barron, T. and O'Neill, C. and Pelayo, R.},679TITLE = {On the computation of delta sets and $\omega$-primality in numerical monoids},680JOURNAL = {preprint},681YEAR = {2014},682}683684@article{GG-MF-VT,685AUTHOR = {Garc\'{\i}a-Garc\'{\i}a, J. I. and Moreno-Fr\'{\i}as, M. A. and Vigneron-Tenorio, A.},686TITLE = {Computation of Delta sets of numerical monoids},687JOURNAL = {Monatsh. Math. },688VOLUME = {178},689PAGES={457--472},690YEAR ={2015},691}692693@misc{Normaliz,694AUTHOR={Bruns, W. and Ichim, B. and R\"omer, T. and S\"oger C.},695TITLE={Normaliz. Algorithms for rational cones and affine monoids},696YEAR={2014},697VERSION={2.12},698howpublished={\url{http://www.math.uos.de/normaliz}},699}700701@misc{Singular,702title = {{\sc Singular} {3-1-6} --- {A} computer algebra system for polynomial computations},703author = {Decker, Wolfram and Greuel, Gert-Martin and Pfister, Gerhard and Sch\"onemann, Hans},704year = {2012},705howpublished = {\url{http://www.singular.uni-kl.de}},706}707708@misc{NmzInterface,709author={Gutsche, S and Horn, M. and S\"oger, C.},710title={NormalizInterface for GAP},711year={2014},712howpublished={\url{https://github.com/fingolfin/NormalizInterface}},713}714715@misc{SingularInterface,716author={Barakat, M. and Horn, M. and Lübeck, F. and Motsak, O. and Neunhoeffer, M. and Schoenemann H.},717title={SingularInterface for GAP},718year={2014},719howpublished={\url{https://github.com/gap-system/SingularInterface.git}},720}721722@misc{Singularpackage,723author={Costantini, M. and de Graaf, W.},724year={2012},725title={GAP package singular; the GAP interface to Singular},726howpublished={\url{http://gap-system.org/Packages/singular.html}},727}728729@article{R-GS-GG-B,730author = {Rosales,J. C. and Garc\'{\i}a-S\'anchez,P. A. and, Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.},731title = {SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS},732journal = {Journal of the London Mathematical Society},733volume = {65},734issue = {03},735month = {6},736year = {2002},737issn = {1469-7750},738pages = {611--623},739numpages = {13},740doi = {10.1112/S0024610701003052},741URL = {http://journals.cambridge.org/article_S0024610701003052},742}743744@article{R-GS,745title = "Nonnegative elements of subgroups of \(\mathbb{Z}^n\)",746journal = "Linear Algebra and its Applications ",747volume = "270",748number = "1-3",749pages = "351- 357",750year = "1998",751note = "",752issn = "0024-3795",753doi = "http://dx.doi.org/10.1016/S0024-3795(97)00309-1",754url = "http://www.sciencedirect.com/science/article/pii/S0024379597003091",755author = "J.C. Rosales and Pedro A. Garc\'{\i}a-S\'anchez",756abstract = "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. "757}758759@article {MR1678508,760AUTHOR = {Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},761TITLE = {On free affine semigroups},762JOURNAL = {Semigroup Forum},763FJOURNAL = {Semigroup Forum},764VOLUME = {58},765YEAR = {1999},766NUMBER = {3},767PAGES = {367--385},768ISSN = {0037-1912},769CODEN = {SMGFAN},770MRCLASS = {13C40 (20M14)},771MRNUMBER = {1678508 (2000j:13020)},772MRREVIEWER = {L{\^e} Tu{\^a}n Hoa},773DOI = {10.1007/BF03325435},774URL = {http://dx.doi.org/10.1007/BF03325435},775}776777@article {MR0269762,778AUTHOR = {Herzog, J{\"u}rgen},779TITLE = {Generators and relations of abelian semigroups and semigroup780rings. },781JOURNAL = {Manuscripta Math.},782FJOURNAL = {Manuscripta Mathematica},783VOLUME = {3},784YEAR = {1970},785PAGES = {175--193},786ISSN = {0025-2611},787MRCLASS = {20.93},788MRNUMBER = {0269762 (42 \#4657)},789MRREVIEWER = {J. B. Kim},790}791792@article {MR1394747,793AUTHOR = {Eisenbud, David and Sturmfels, Bernd},794TITLE = {Binomial ideals},795JOURNAL = {Duke Math. J.},796FJOURNAL = {Duke Mathematical Journal},797VOLUME = {84},798YEAR = {1996},799NUMBER = {1},800PAGES = {1--45},801ISSN = {0012-7094},802CODEN = {DUMJAO},803MRCLASS = {13P10 (13A30 14M25)},804MRNUMBER = {1394747 (97d:13031)},805MRREVIEWER = {P. Schenzel},806DOI = {10.1215/S0012-7094-96-08401-X},807URL = {http://dx.doi.org/10.1215/S0012-7094-96-08401-X},808}809@Misc{4ti2,810author = {4ti2 team},811title = {4ti2---A software package for algebraic, geometric and812combinatorial problems on linear spaces},813howpublished = {{A}vailable at www.4ti2.de}814}815816@Misc{4ti2Interface,817author = {S. Gutsche},818title = {4ti2Interface, A link to 4ti2},819howpublished = {\url{http://www.gap-system.org/Packages/4ti2interface.html}}820}821822@misc{ GradedModules,823author = {Barakat, M. and Gutsche, S. and Jambor, S. and824Lange-Hegermann, M. and Lorenz, A. and Motsak, O.},825title = {{GradedModules}, A homalg based package for the Abelian826category of finitely presented graded modules over827computable graded rings, {V}ersion 2014.09.17},828month = {Sep},829year = {2014},830note = {GAP package},831howpublished = {\href832{http://homalg.math.rwth-aachen.de/~barakat/homalg-project/Gr\833adedModules/}834{\texttt{http://homalg.math.rwth-aachen.de/}\discretionary835{}{}{}\texttt{\texttt{\symbol{126}}barakat/}\discretionary836{}{}{}\texttt{homalg-project/}\discretionary837{}{}{}\texttt{GradedModules/}}},838keywords = {modules; graded modules; graduation; multi-graded modules;839Tate resolution},840printedkey = {BGJLLM14}841}842843@article{DGSRP15,844author = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P.~A. and Robles-P{\'e}rez, A.~M.},845title = {Numerical semigroups with a given set of pseudo-Frobenius numbers},846journal = {LMS J. Comput. Math.},847keywords = {Mathematics - Commutative Algebra, Mathematics - Combinatorics, 11D07, 20M14, 20-04},848year = {2016},849volume= {19},850pages={186--205}851}852853@article{GSONW,854AUTHOR = {Garc\'{\i}a-S\'anchez, P. A. and O'Neill, C. and Webb, G.},855TITLE = {On the computation of factorization invariants for affine semigroups},856JOURNAL = {arxiv:1504.02998},857YEAR ={2017},858URL= {http://arxiv.org/abs/1504.02998},859}860861@article{E,862AUTHOR = {Eliahou, S.},863TITLE = {Wilf's conjecture and {M}acaulay's theorem},864JOURNAL = {preprint},865YEAR = {2015},866}867868869@article {Wilf,870AUTHOR = {Wilf, Herbert S.},871TITLE = {A circle-of-lights algorithm for the ``money-changing872problem''},873JOURNAL = {Amer. Math. Monthly},874FJOURNAL = {The American Mathematical Monthly},875VOLUME = {85},876YEAR = {1978},877NUMBER = {7},878PAGES = {562--565},879ISSN = {0002-9890},880MRCLASS = {10A30 (05A17 68A10)},881MRNUMBER = {0556658 (58 \#27728)},882MRREVIEWER = {Dennis White},883}884885@article{Stokes,886AUTHOR = {Stokes, K.},887TITLE = {Patterns of ideals of numerical semigroups},888JOURNAL = {preprint},889YEAR = {2015},890}891892@article {K-W,893AUTHOR = {Kunz, E. and Waldi, R.},894TITLE = {Geometrical illustration of numerical semigroups and of some895of their invariants},896JOURNAL = {Semigroup Forum},897FJOURNAL = {Semigroup Forum},898VOLUME = {89},899YEAR = {2014},900NUMBER = {3},901PAGES = {664--691},902ISSN = {0037-1912},903MRCLASS = {20M14},904MRNUMBER = {3274840},905MRREVIEWER = {Kurt D. Herzinger},906DOI = {10.1007/s00233-014-9599-7},907URL = {http://dx.doi.org/10.1007/s00233-014-9599-7},908}909910@article{DGSM,911AUTHOR = {D'Anna, M. and Garc{\'{\i}}a-S{\'a}nchez, P.~A. and Micale, E.},912TITLE = {Good semigroups},913JOURNAL = {preprint},914YEAR = {2016},915}916917@article {MC-O-T,918AUTHOR = {M{\'a}rquez-Campos, Guadalupe and Ojeda, Ignacio and Tornero,919Jos{\'e} M.},920TITLE = {On the computation of the {A}p\'ery set of numerical monoids921and affine semigroups},922JOURNAL = {Semigroup Forum},923FJOURNAL = {Semigroup Forum},924VOLUME = {91},925YEAR = {2015},926NUMBER = {1},927PAGES = {139--158},928ISSN = {0037-1912},929MRCLASS = {20M14},930MRNUMBER = {3369384},931MRREVIEWER = {Andreas Reinhart},932DOI = {10.1007/s00233-014-9631-y},933URL = {http://dx.doi.org/10.1007/s00233-014-9631-y},934}935936937@article {Roune,938AUTHOR = {Roune, Bjarke Hammersholt},939TITLE = {Solving thousand-digit {F}robenius problems using {G}r\"obner940bases},941JOURNAL = {J. Symbolic Comput.},942FJOURNAL = {Journal of Symbolic Computation},943VOLUME = {43},944YEAR = {2008},945NUMBER = {1},946PAGES = {1--7},947ISSN = {0747-7171},948MRCLASS = {13P10 (13D40 68W30)},949MRNUMBER = {2381966},950MRREVIEWER = {Giancarlo Rinaldo},951DOI = {10.1016/j.jsc.2007.06.002},952URL = {http://dx.doi.org/10.1016/j.jsc.2007.06.002},953}954955@article{Ugolini,956author = {Ugolini, Simone},957title = {On numerical semigroups closed with respect to the action of affine maps},958journal= "arXiv",959volume= "1505.06580",960year= "2016"961}962963@article {MR3493240,964AUTHOR = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},965TITLE = {{numericalsgps}, a {GAP} package for numerical966semigroups},967JOURNAL = {ACM Commun. Comput. Algebra},968FJOURNAL = {ACM Communications in Computer Algebra},969VOLUME = {50},970YEAR = {2016},971NUMBER = {1},972PAGES = {12--24},973ISSN = {1932-2232},974MRCLASS = {20-04 (20M14 68W30)},975MRNUMBER = {3493240},976}977978@article {arf-frob-gen,979AUTHOR={Garc{\'{\i}}a-S{\'a}nchez, P. A. and Heredia, B. A. and Karakas, H. I. and Rosales, J. C.},980TITLE = {Parametrizing Arf numerical semigroups},981JOURNAL = {J. Algebra Appl.},982VOLUME = {16},983YEAR = {2017},984PAGES = {1750209 (31 pages)}985}986987@article {duplication,988AUTHOR = {D'Anna, M. and Strazzanti, F.},989TITLE = {The numerical duplication of a numerical semigroup},990JOURNAL = {Semigroup Forum},991FJOURNAL = {Semigroup Forum},992VOLUME = {87},993YEAR = {2013},994NUMBER = {1},995PAGES = {149--160},996ISSN = {0037-1912},997MRCLASS = {20M12 (06B10 13A15 13A30 13F10 16D25)},998MRNUMBER = {3079777},999MRREVIEWER = {Paula M. Machado Cruz Catarino},1000DOI = {10.1007/s00233-012-9451-x},1001URL = {http://dx.doi.org/10.1007/s00233-012-9451-x},1002}10031004@article {DA-G-H,1005AUTHOR = {D'Anna, Marco and Guerrieri, Anna and Heinzer, William},1006TITLE = {Invariants of ideals having principal reductions},1007JOURNAL = {Comm. Algebra},1008FJOURNAL = {Communications in Algebra},1009VOLUME = {29},1010YEAR = {2001},1011NUMBER = {2},1012PAGES = {889--906},1013ISSN = {0092-7872},1014MRCLASS = {13A15 (13C10)},1015MRNUMBER = {1842007},1016MRREVIEWER = {L. J. Ratliff, Jr.},1017DOI = {10.1081/AGB-100001550},1018URL = {http://dx.doi.org/10.1081/AGB-100001550},1019}10201021@article {Br-acute,1022AUTHOR = {Bras-Amor\'os, Maria},1023TITLE = {Acute semigroups, the order bound on the minimum distance, and1024the {F}eng-{R}ao improvements},1025JOURNAL = {IEEE Trans. Inform. Theory},1026FJOURNAL = {Institute of Electrical and Electronics Engineers.1027Transactions on Information Theory},1028VOLUME = {50},1029YEAR = {2004},1030NUMBER = {6},1031PAGES = {1282--1289},1032ISSN = {0018-9448},1033MRCLASS = {20M14 (94B27)},1034MRNUMBER = {2094884},1035DOI = {10.1109/TIT.2004.828104},1036URL = {http://dx.doi.org/10.1109/TIT.2004.828104},1037}103810391040@article {A-A-GS,1041AUTHOR = {Abbas, A. and Assi, A. and García-Sánchez, P. A.},1042TITLE = {Canonical bases of modules over one dimensional k-algebras},1043JOURNAL = {arxiv:1703.02825},1044YEAR ={2017},1045URL= {http://arxiv.org/abs/1703.02825},1046}10471048@Article{DelgadoFarranGarcia-SanchezLlena2013MC,1049Title = {{On the generalized Feng-Rao numbers of numerical semigroups generated by intervals}},1050Author = {{Delgado}, M. and {Farr{\'a}n}, J.~I. and {Garc{\'{\i}}a-S{\'a}nchez}, P.~A. and {Llena}, D.},1051Journal = {Mathematics of Computation},1052Year = {2013},1053Number = {283},1054Pages = {1813--1836},1055Volume = {82},10561057Adsnote = {Provided by the SAO/NASA Astrophysics Data System},1058Adsurl = {http://adsabs.harvard.edu/abs/2011arXiv1105.4833D},1059Archiveprefix = {arXiv},1060Doi = {http://dx.doi.org/10.1090/S0025-5718-2013-02673-7},1061Eprint = {1105.4833},1062Keywords = {Mathematics - Number Theory, 20M14, 11Y55, 11T71},1063Primaryclass = {math.NT}1064}106510661067