{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T11:30:20Z","timestamp":1748431820711},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"04","license":[{"start":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T00:00:00Z","timestamp":1545868800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>C<\/jats:italic> be a set of positive integers. In this paper, we obtain an algorithm for computing all subsets <jats:italic>A<\/jats:italic> of positive integers which are minimals with the condition that if <jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub> + \u2026 + <jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> is a partition of an element in <jats:italic>C<\/jats:italic>, then at least a summand of this partition belongs to <jats:italic>A<\/jats:italic>. We use techniques of numerical semigroups to solve this problem because it is equivalent to give an algorithm that allows us to compute all the numerical semigroups which are maximals with the condition that has an empty intersection with the set <jats:italic>C<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/prm.2018.65","type":"journal-article","created":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T05:43:36Z","timestamp":1545889416000},"page":"969-978","source":"Crossref","is-referenced-by-count":3,"title":["A problem of integer partitions and numerical semigroups"],"prefix":"10.1017","volume":"149","author":[{"given":"J. C.","family":"Rosales","sequence":"first","affiliation":[]},{"given":"M. B.","family":"Branco","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,12,27]]},"reference":[{"key":"S0308210518000653_ref9","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568209.001.0001"},{"key":"S0308210518000653_ref8","doi-asserted-by":"publisher","DOI":"10.2307\/121118"},{"key":"S0308210518000653_ref7","first-page":"443","volume":"5","author":"Jim\u00e9nez Urroz","year":"2002","journal-title":"LA Gaceta RSME"},{"key":"S0308210518000653_ref6","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-17.1.75"},{"key":"S0308210518000653_ref4","doi-asserted-by":"publisher","DOI":"10.1515\/form.2011.151"},{"key":"S0308210518000653_ref10","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2003.209.131"},{"key":"S0308210518000653_ref2","first-page":"1198","volume":"222","author":"Ap\u00e9ry","year":"1946","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S0308210518000653_ref1","volume-title":"The theory of partitions, encyclopedia of mathematics and its applications","author":"Andrews","year":"1985"},{"key":"S0308210518000653_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-002-0007-3"},{"key":"S0308210518000653_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0160-6"},{"key":"S0308210518000653_ref3","first-page":"78","volume":"598","author":"Barucci","year":"1997","journal-title":"Memoirs of the Amer. Math. Soc."}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210518000653","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T07:55:21Z","timestamp":1564732521000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210518000653\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,27]]},"references-count":11,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["S0308210518000653"],"URL":"https:\/\/doi.org\/10.1017\/prm.2018.65","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,27]]}}}