{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T15:53:28Z","timestamp":1720281208091},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2013,9]]},"abstract":" Patterns on numerical semigroups are multivariate linear polynomials, and they are said to admit a numerical semigroup if evaluating the pattern at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns were analyzed. In this contribution we study conditions for a nonhomogeneous pattern to admit a nontrivial numerical semigroup, and particularize this study to the case the independent term of the pattern is a multiple of the multiplicity of the semigroup. Moreover, for the so-called strongly admissible patterns, the set of numerical semigroups admitting these patterns with fixed multiplicity m forms an m-variety, which allows us to represent this set in a tree and to describe minimal sets of generators of the semigroups in the variety with respect to the pattern. Furthermore, we characterize strongly admissible patterns having a finite associated tree. <\/jats:p>","DOI":"10.1142\/s0218196713500306","type":"journal-article","created":{"date-parts":[[2013,7,4]],"date-time":"2013-07-04T08:07:23Z","timestamp":1372925243000},"page":"1469-1483","source":"Crossref","is-referenced-by-count":12,"title":["NONHOMOGENEOUS PATTERNS ON NUMERICAL SEMIGROUPS"],"prefix":"10.1142","volume":"23","author":[{"given":"MARIA","family":"BRAS-AMOR\u00d3S","sequence":"first","affiliation":[{"name":"Departament d'Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Av. Pa\u00efsos Catalans, 26 Campus Sescelades, Tarragona 43007, Espa\u00f1a, Spain"}]},{"given":"PEDRO A.","family":"GARC\u00cdA-S\u00c1NCHEZ","sequence":"additional","affiliation":[{"name":"Departamento de \u00c1lgebra, Universidad de Granada, Granada E-18071, Espa\u00f1a, Spain"}]},{"given":"ALBERT","family":"VICO-OTON","sequence":"additional","affiliation":[{"name":"Departament d'Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Av. Pa\u00efsos Catalans, 26 Campus Sescelades, Tarragona 43007, Espa\u00f1a, Spain"}]}],"member":"219","published-online":{"date-parts":[[2013,9,19]]},"reference":[{"key":"rf1","first-page":"x+78","volume":"125","author":"Barucci V.","year":"1997","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-012-9685-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44828-4_22"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.828104"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.11.007"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-006-0015-8"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-011-9343-5"},{"key":"rf8","author":"Bras-Amor\u00f3s M.","year":"2012","journal-title":"Des. Codes Cryptogr."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/18.887872"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-008-9049-5"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2008.11.013"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/103"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(90)90041-F"},{"key":"rf14","first-page":"469","volume":"34","author":"Rosales J. C.","year":"2003","journal-title":"Houston J. Math."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2008-015-6"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0160-6"},{"key":"rf17","first-page":"47","volume":"2","author":"Rosales J. C.","year":"2003","journal-title":"Int. J. Commut. Rings"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.03.007"},{"key":"rf19","first-page":"321","volume":"30","author":"Rosales J. C.","year":"2004","journal-title":"Houston J. Math."},{"key":"rf20","author":"Stokes K.","year":"2013","journal-title":"Semigroup Forum"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2003-045-8"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196713500306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:11:57Z","timestamp":1565197917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196713500306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":21,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2013,9,19]]},"published-print":{"date-parts":[[2013,9]]}},"alternative-id":["10.1142\/S0218196713500306"],"URL":"https:\/\/doi.org\/10.1142\/s0218196713500306","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}