{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T21:20:20Z","timestamp":1778361620075,"version":"3.51.4"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"301","license":[{"start":{"date-parts":[[2016,12,31]],"date-time":"2016-12-31T00:00:00Z","timestamp":1483142400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-12-BS01-0017"],"award-info":[{"award-number":["ANR-12-BS01-0017"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well-suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing very large optimizations: we obtain the number of numerical semigroups of genus\n \n \n \n \n g<\/mml:mi>\n \n \u2a7d\n \n <\/mml:mo>\n 67<\/mml:mn>\n <\/mml:mrow>\n g\\leqslant 67<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and we confirm the Wilf conjecture for\n \n \n \n \n g<\/mml:mi>\n \n \u2a7d\n \n <\/mml:mo>\n 60<\/mml:mn>\n <\/mml:mrow>\n g\\leqslant 60<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/mcom\/3075","type":"journal-article","created":{"date-parts":[[2015,11,18]],"date-time":"2015-11-18T09:44:46Z","timestamp":1447839886000},"page":"2553-2568","source":"Crossref","is-referenced-by-count":34,"title":["Exploring the tree of numerical semigroups"],"prefix":"10.1090","volume":"85","author":[{"given":"Jean","family":"Fromentin","sequence":"first","affiliation":[]},{"given":"Florent","family":"Hivert","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2015,12,31]]},"reference":[{"key":"1","first-page":"767","article-title":"Generating tuples of integers modulo the action of a permutation group and applications","author":"Borie, Nicolas","year":"2013"},{"key":"2","isbn-type":"print","first-page":"21","article-title":"Addition behavior of a numerical semigroup","author":"Bras-Amor\u00f3s, Maria","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/2856291759"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s00233-007-9014-8","article-title":"Fibonacci-like behavior of the number of numerical semigroups of a given genus","volume":"76","author":"Bras-Amor\u00f3s, Maria","year":"2008","journal-title":"Semigroup Forum","ISSN":"https:\/\/id.crossref.org\/issn\/0037-1912","issn-type":"print"},{"key":"4","unstructured":"M. Delgado, Homepage, \\url{http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/numbers\/}."},{"key":"5","unstructured":"M. Delgado, P. A. Garci\u00e1-S\u00e1nchez, and J. Morais, NumericalSgps, A GAP package for numerical semigroups. Available via \\url{http:\/\/www.gap-system.org}."},{"key":"6","unstructured":"J. Fromentin and F. Hivert, \\url{https:\/\/github.com\/jfromentin\/nsgtree}."},{"key":"7","unstructured":"The GAP Group, GAP \u2013 Groups, Algorithms, and Programming, Version 4.7.7, 2015."},{"key":"8","unstructured":"M. Girkar, Intel instruction set architecture extensions | Intel\u00ae developer zone, Software.intel.com, 2013."},{"key":"9","unstructured":"B. V. Iyer, R. Geva, and P. Halpern, Cilk\u2122 plus in gcc, GNU Tools Cauldron, 2012."},{"key":"10","series-title":"Oxford Lecture Series in Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568209.001.0001","volume-title":"The Diophantine Frobenius problem","volume":"30","author":"Ram\u00edrez Alfons\u00edn, J. L.","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/9780198568209"},{"key":"11","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.laa.2005.03.014","article-title":"Fundamental gaps of numerical semigroups generated by two elements","volume":"405","author":"Rosales, J. C.","year":"2005","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"12","series-title":"Developments in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0160-6","volume-title":"Numerical semigroups","volume":"20","author":"Rosales, J. C.","year":"2009","ISBN":"https:\/\/id.crossref.org\/isbn\/9781441901590"},{"key":"13","unstructured":"N. J. A. Sloane, The on-line encyclopedia of integer sequences, \\url{http:\/\/oeis.org\/}."},{"key":"14","unstructured":"Software.intel.com, Intel\u00ae Cilk\u2122 homepage, \\url{https:\/\/www.cilkplus.org\/}, 2013."},{"key":"15","unstructured":"Software.intel.com, Intel\u00ae Cilk\u2122 plus reference guide, \\url{https:\/\/software.intel.com\/en-us\/node\/522579}, 2013."},{"key":"16","unstructured":"Wikipedia, Advanced vector extension, \\url{http:\/\/en.wikipedia.org\/wiki\/Advanced_{V}ector_{E}xtensions}, 2014."},{"key":"17","unstructured":"Wikipedia, Duff\u2019s device, \\url{http:\/\/en.wikipedia.org\/wiki\/Duff\u2019s_{d}evice}, 2014."},{"key":"18","unstructured":"Wikipedia, Hyper-threading, \\url{http:\/\/en.wikipedia.org\/wiki\/Hyper-Threading}, 2014."},{"key":"19","unstructured":"Wikipedia, Simd, \\url{http:\/\/en.wikipedia.org\/wiki\/SIMD}, 2014."},{"key":"20","unstructured":"Wikipedia, Streaming simd extensions, \\url{http:\/\/en.wikipedia.org\/wiki\/Streaming_{S}IMD_{E}xtensions}, 2014."},{"key":"21","unstructured":"Wikipedia, Turbo boost, \\url{http:\/\/en.wikipedia.org\/wiki\/Intel_{T}urbo_{B}oost}, 2014."},{"issue":"7","key":"22","doi-asserted-by":"publisher","first-page":"562","DOI":"10.2307\/2320864","article-title":"A circle-of-lights algorithm for the \u201cmoney-changing problem\u201d","volume":"85","author":"Wilf, Herbert S.","year":"1978","journal-title":"Amer. 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Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"issue":"3","key":"23","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1007\/s00233-012-9456-5","article-title":"Fibonacci-like growth of numerical semigroups of a given genus","volume":"86","author":"Zhai, Alex","year":"2013","journal-title":"Semigroup Forum","ISSN":"https:\/\/id.crossref.org\/issn\/0037-1912","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-301\/S0025-5718-2015-03075-0\/S0025-5718-2015-03075-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-301\/S0025-5718-2015-03075-0\/S0025-5718-2015-03075-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:53:58Z","timestamp":1776797638000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-301\/S0025-5718-2015-03075-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,31]]},"references-count":23,"journal-issue":{"issue":"301","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["S0025-5718-2015-03075-0"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3075","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2015,12,31]]}}}