{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:29:16Z","timestamp":1772252956782,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,11]],"date-time":"2021-12-11T00:00:00Z","timestamp":1639180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Ciencia e Innovaci\u00f3n. Spain","award":["PGC2018-096446-B-C21"],"award-info":[{"award-number":["PGC2018-096446-B-C21"]}]},{"name":"Ministerio de Ciencia e Innovaci\u00f3n. Spain","award":["MTM2017-84890-P"],"award-info":[{"award-number":["MTM2017-84890-P"]}]},{"name":"Junta de Extremadura\/FEDER-funds","award":["GR18001. FQM-024"],"award-info":[{"award-number":["GR18001. FQM-024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>Let a,b and n&gt;1 be three positive integers such that a and \u2211j=0n\u22121bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by {\u2211j=0n\u22121bj}\u222a{\u2211j=0n\u22121bj+a\u2211j=0i\u22122bj\u2223i=2,\u2026,n} is determinantal. Moreover, we prove that for n&gt;3, the ideal I has a unique minimal system of generators if and only if a&lt;b\u22121.<\/jats:p>","DOI":"10.3390\/math9243204","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T01:29:33Z","timestamp":1639358973000},"page":"3204","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0397-7602","authenticated-orcid":false,"given":"Manuel B.","family":"Branco","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidade de \u00c9vora, 7000-671 Evora, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5297-6791","authenticated-orcid":false,"given":"Isabel","family":"Cola\u00e7o","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica e Ci\u00eancias F\u00edsicas, Instituto Polit\u00e9cnico de Beja, 7800-295 Beja, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3173-5934","authenticated-orcid":false,"given":"Ignacio","family":"Ojeda","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,11]]},"reference":[{"key":"ref_1","unstructured":"Stratton, J.A. 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