间隙集扩展、理论与计算

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-05 DOI:arxiv-2408.02425

Arman Ataei Kachouei, Farhad Rahmati

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引用次数: 0

摘要

在本文中，我们将数字半群的一些集合论概念扩展到自然数的任意子半群。最后，我们介绍了缺口集的扩展，并证明这些大小为 $g$ 的缺口集的数量序列是不递减的，这是 Bras-Amor\'os 猜想的弱版本。

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Gapset Extensions, Theory and Computations

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.

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arXiv - MATH - Commutative Algebra

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