{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:11Z","timestamp":1760234771726,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T00:00:00Z","timestamp":1623888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003030","name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","doi-asserted-by":"publisher","award":["2017 SGR 00705"],"award-info":[{"award-number":["2017 SGR 00705"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Spanish Ministry of Economy and Competitivity","award":["TIN2016-80250-R"],"award-info":[{"award-number":["TIN2016-80250-R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we present the notion of the quasi-ordinarization transform of a numerical semigroup. The set of all semigroups of a fixed genus can be organized in a forest whose roots are all the quasi-ordinary semigroups of the same genus. This way, we approach the conjecture on the increasingness of the cardinalities of the sets of numerical semigroups of each given genus. We analyze the number of nodes at each depth in the forest and propose new conjectures. Some properties of the quasi-ordinarization transform are presented, as well as some relations between the ordinarization and quasi-ordinarization transforms.<\/jats:p>","DOI":"10.3390\/sym13061084","type":"journal-article","created":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T21:29:16Z","timestamp":1623965356000},"page":"1084","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Ordinarization Transform of a Numerical Semigroup"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3481-004X","authenticated-orcid":false,"given":"Maria","family":"Bras-Amor\u00f3s","sequence":"first","affiliation":[{"name":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3569-3885","authenticated-orcid":false,"given":"Hebert","family":"P\u00e9rez-Ros\u00e9s","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8140-1169","authenticated-orcid":false,"given":"Jos\u00e9 Miguel","family":"Serradilla-Merinero","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.1007\/s10910-016-0653-4","article-title":"Semigroup theory of symmetry","volume":"54","author":"Rosenfeld","year":"2016","journal-title":"J. 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