The genus of a quotient of several types of numerical semigroups

被引：0
作者：
Lee, Kyeongjun [1 ]
Nam, Hayan [2 ]
机构：
[1] Yonsei Univ, Dept Math, Seoul, South Korea
[2] Duksung Womens Univ, Dept Math, Seoul, South Korea
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2024年 / 20卷 / 07期
基金：
新加坡国家研究基金会;
关键词：
Numerical semigroups; quotient of numerical semigroups; genus;
D O I：
10.1142/S1793042124500891
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Finding the Frobenius number and the genus of any numerical semigroup S is a well-known open problem. Similarly, it has been studied how to express the Frobenius number and the genus of a quotient of a numerical semigroup. In this paper, by enumerating the Hilbert series of each type of numerical semigroup, we show an expression for the genus of a quotient of numerical semigroups generated by one of the following series: arithmetic progression, geometric series, and Pythagorean triple.
引用
收藏
页码：1809 / 1831
页数：23
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