{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:57:05Z","timestamp":1768352225399,"version":"3.49.0"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2016,4,1]],"date-time":"2016-04-01T00:00:00Z","timestamp":1459468800000},"content-version":"unspecified","delay-in-days":91,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.<\/jats:p>","DOI":"10.1112\/s1461157016000061","type":"journal-article","created":{"date-parts":[[2016,4,25]],"date-time":"2016-04-25T09:54:55Z","timestamp":1461578095000},"page":"186-205","source":"Crossref","is-referenced-by-count":5,"title":["Numerical semigroups with a given set of\u00a0pseudo-Frobenius\u00a0numbers"],"prefix":"10.1112","volume":"19","author":[{"given":"M.","family":"Delgado","sequence":"first","affiliation":[]},{"given":"P. A.","family":"Garc\u00eda-S\u00e1nchez","sequence":"additional","affiliation":[]},{"given":"A. M.","family":"Robles-P\u00e9rez","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2016,4,1]]},"reference":[{"key":"S1461157016000061_r2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01170309"},{"key":"S1461157016000061_r7","unstructured":"7. A. M. Robles-P\u00e9rez and J. C. Rosales , \u2018The genus, the Frobenius number, and the pseudo-Frobenius numbers of numerical semigroups with type two\u2019, Proc. Roy. Soc. Edinburgh Sect. A, to appear."},{"key":"S1461157016000061_r3","unstructured":"3. M. Delgado , \u2018intpic, a GAP package for drawing integers\u2019, http:\/\/www.gap-system.org\/."},{"key":"S1461157016000061_r5","unstructured":"5. The GAP\u00a0group, \u2018GAP \u2013 Groups, algorithms, programming\u2019, version 4.7.7, 2015, http:\/\/www.gap-system.org\/."},{"key":"S1461157016000061_r8","volume-title":"Numerical Semigroups","volume":"20","author":"Rosales","year":"2010"},{"key":"S1461157016000061_r1","doi-asserted-by":"publisher","DOI":"10.1515\/form.2011.151"},{"key":"S1461157016000061_r6","doi-asserted-by":"publisher","DOI":"10.21099\/tkbjm\/1496159535"},{"key":"S1461157016000061_r4","doi-asserted-by":"crossref","unstructured":"4. M. Delgado , P. A. Garc\u00eda-S\u00e1nchez and J. Morais , \u2018NumericalSgps, a GAP package for numerical semigroups\u2019, version 1.0.1, 2015, http:\/\/www.gap-system.org\/.","DOI":"10.1145\/2930964.2930966"},{"key":"S1461157016000061_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2003.10.024"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157016000061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T00:40:08Z","timestamp":1567816808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157016000061\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016]]}},"alternative-id":["S1461157016000061"],"URL":"https:\/\/doi.org\/10.1112\/s1461157016000061","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}