Geodesic
Compositions of a numerical semigroup
Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 77-83

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Given a numerical semigroup $S$, a nonnegative integer $a$ and $m\in S\backslash\{0\}$, we introduce the set $C(S,a,m)=\{s+aw(s~mod~m)~|~s\in S\}$, where $\{w(0), w(1), \cdots, w(m-1)\}$ is the Apéry set of $m$ in $S$. In this paper we characterize the pairs $(a,m)$ such that $C(S,a,m)$ is a numerical semigroup. We study the principal invariants of $C(S,a,m)$ which are given explicitly in terms of invariants of $S$. We also characterize the compositions $C(S,a,m)$ that are symmetric, pseudo-symmetric and almost symmetric. Finally, a result about compliance to Wilf's conjecture of $C(S,a,m)$ is given.
Keywords: numerical semigroups, compositions, Apéry sets, Frobenius number, Wilf's conjecture. 
@article{DM_2019_31_2_a6,
     author = {Ze Gu},
     title = {Compositions of a numerical semigroup},
     journal = {Diskretnaya Matematika},
     pages = {77--83},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_2_a6/}
}
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Ze Gu. Compositions of a numerical semigroup. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 77-83. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a6/