GENERATING FUNCTIONS FOR THE QUOTIENTS OF NUMERICAL SEMIGROUPS

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-02-29 DOI:10.1017/s0004972724000054

FEIHU LIU

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引用次数: 0

Abstract

We propose generating functions,

$\textrm {RGF}_p(x)$

, for the quotients of numerical semigroups which are related to the Sylvester denumerant. Using MacMahon’s partition analysis, we can obtain

$\textrm {RGF}_p(x)$

by extracting the constant term of a rational function. We use

$\textrm {RGF}_p(x)$

to give a system of generators for the quotient of the numerical semigroup

$\langle a_1,a_2,a_3\rangle $

by p for a small positive integer p, and we characterise the generators of

${\langle A\rangle }/{p}$

for a general numerical semigroup A and any positive integer p.

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数值半群商数的生成函数

我们提出了与西尔维斯特数数相关的数值半群商数的生成函数 $\textrm {RGF}_p(x)$ 。利用麦克马洪的分割分析，我们可以通过提取有理函数的常数项得到 $\textrm {RGF}_p(x)$ 。我们利用 $\textrm {RGF}_p(x)$ 给出了一个小正整数 p 的数值半群 $\langle a_1,a_2,a_3\rangle $ 的商的生成器系统，并描述了一般数值半群 A 和任意正整数 p 的 ${\langle A\rangle }/{p}$ 的生成器的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society