Arman Ataei Kachouei, Farhad Rahmati
Published 2024-08-05Version 1
In this paper we extend some set theoretic concepts of numerical semigroups for arbitrary sub-semigroups of natural numbers. Then we characterized gapsets which leads to a more efficient computational approach towards numerical semigroups and finally we introduce the extension of gapsets and prove that the sequence of the number of gapsets of size $g$ is non-decreasing as a weak version of Bras-Amor\'os's conjecture.
Comments: 14 pages, 2 algorithms
$p$-numerical semigroups with $p$-symmetric properties
Improved bounds on the number of numerical semigroups of a given genus
Computing the number of numerical semigroups using generating functions
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