TELESCOPIC NUMERICAL SEMIGROUPS WITH MULTIPLICITY TEN AND EMBEDDING DIMENSION THREE
نویسندگان
چکیده
In this work, we give parametrizations of telescopic numerical semigroups with multiplicity ten and embedding dimension three.
 We also express some its invariants in terms generators these such as the Frobenius number, genus Sylvester number.
منابع مشابه
on numerical semigroups with embedding dimension three
let $fneq1,3$ be a positive integer. we prove that there exists a numerical semigroup $s$ with embedding dimension three such that $f$ is the frobenius number of $s$. we also show that the same fact holds for affine semigroups in higher dimensional monoids.
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متن کاملOn Numerical Semigroups with Embedding Dimension Three
Let f ̸= 1, 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.
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Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.
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Even though the study and relevance of maximal embedding dimension numerical semigroups arises in a natural way among the other numerical semigroups, they have become specially renowned due to the existing applications to commutative algebra via their associated semigroup ring (see for instance [1, 5, 15, 16, 99, 100]). They are a source of examples of commutative rings with some maximal proper...
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ژورنال
عنوان ژورنال: Journal of universal mathematics
سال: 2022
ISSN: ['2618-5660']
DOI: https://doi.org/10.33773/jum.1098406