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- W4378506955 abstract "In this work we will show that if $F$ is a positive integer, then ${mathrm{Sat}}(F)={Smid S mbox{ is a saturated numerical semigroup with Frobenius number } F}$ is a covariety. As a consequence, we present two algorithms: one that computes ${mathrm{Sat}}(F),$ and the other which computes all the elements of ${mathrm{Sat}}(F)$ with a fixed genus. If $Xsubseteq Sbackslash Delta(F)$ for some $Sin {mathrm{Sat}}(F),$ then we will see that there is the least element of ${mathrm{Sat}}(F)$ containing a $X$. This element will denote by ${mathrm{Sat}}(F)[X].$ If $Sin{mathrm{Sat}}(F),$ then we define the ${mathrm{Sat}}(F)$-rank of $S$ as the minimum of ${mbox{cardinality}(X)mid S={mathrm{Sat}}(F)[X]}.$ In this paper, also we present an algorithm to compute all the element of ${mathrm{Sat}}(F)$ with a given ${mathrm{Sat}}(F)$-rank." @default.
- W4378506955 created "2023-05-27" @default.
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- W4378506955 date "2023-05-23" @default.
- W4378506955 modified "2023-09-30" @default.
- W4378506955 title "The covariety of saturated numerical semigroups with fixed Frobenius number" @default.
- W4378506955 doi "https://doi.org/10.48550/arxiv.2305.13881" @default.
- W4378506955 hasPublicationYear "2023" @default.
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