Almost Symmetric Numerical Semigroups with Odd Generators

Strazzanti, Francesco; Watanabe, Kei-ichi

doi:10.1007/978-3-030-40822-0_19

Cited by 4 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first inequality was proved in [2], and the second in [5]. Numerical semigroups that satisfy t(S) = 2g(S)−F (S) are called almost symmetric, this notion was introduced in [6] and has been studied in several papers [5,7,8,9,10,11,12]. It is known that all irreducible numerical semigroups are almost symmetric.…”

Section: Introductionmentioning

confidence: 99%

Numerical Semigroups of small and large type

Singhal¹

2020

Preprint

View full text Add to dashboard Cite

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number F, genus g and type t. It is known that for any numerical semigroup g F +1−g ≤ t ≤ 2g − F . Numerical semigroups with t = 2g − F are called almost symmetric, we introduce a new property that characterises them. We give an explicit characterisation of numerical semigroups with t = g F +1−g . We show that for a fixed α the number of numerical semigroups with Frobenius number F and type F − α is eventually constant for large F . Also the number of numerical semigroups with genus g and type g − α is also eventually constant for large g.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical Semigroups of small and large type

Singhal¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Many papers deal with the almost symmetric property and how to construct examples of these semigroups (see for instance [3,4,11] and the references therein). Some manuscripts like [11,12] and [15] deal with almost symmetric numerical semigroups with small type and small embedding dimension, which is the cardinality of a minimal generating set of the numerical semigroup. The semigroups considered in this manuscript have large type.…”

Section: Introductionmentioning

confidence: 99%