{"title":"缺口集和 k 个广义斐波那契序列","authors":"Gilberto B. Almeida Filho, Matheus Bernardini","doi":"10.1142/s0218196724500085","DOIUrl":null,"url":null,"abstract":"<p>We bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to <i>m</i>-extensions. It allows us to identify gapsets and, in general, <i>m</i>-extensions with tilings of boards; as a consequence, we present some applications of this identification. Moreover, we present explicit formulas for the number of gapsets with fixed genus and depth, when the multiplicity is 3 or 4, and, in some cases, for the number of gapsets with fixed genus and depth.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gapsets and the k-generalized Fibonacci sequences\",\"authors\":\"Gilberto B. Almeida Filho, Matheus Bernardini\",\"doi\":\"10.1142/s0218196724500085\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to <i>m</i>-extensions. It allows us to identify gapsets and, in general, <i>m</i>-extensions with tilings of boards; as a consequence, we present some applications of this identification. Moreover, we present explicit formulas for the number of gapsets with fixed genus and depth, when the multiplicity is 3 or 4, and, in some cases, for the number of gapsets with fixed genus and depth.</p>\",\"PeriodicalId\":13756,\"journal\":{\"name\":\"International Journal of Algebra and Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Algebra and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218196724500085\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Algebra and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218196724500085","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to m-extensions. It allows us to identify gapsets and, in general, m-extensions with tilings of boards; as a consequence, we present some applications of this identification. Moreover, we present explicit formulas for the number of gapsets with fixed genus and depth, when the multiplicity is 3 or 4, and, in some cases, for the number of gapsets with fixed genus and depth.
期刊介绍：
The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.
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