{"title":"几类数字半群商数的属数","authors":"Kyeongjun Lee, Hayan Nam","doi":"10.1142/s1793042124500891","DOIUrl":null,"url":null,"abstract":"<p>Finding the Frobenius number and the genus of any numerical semigroup <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>S</mi></math></span><span></span> 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.</p>","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The genus of a quotient of several types of numerical semigroups\",\"authors\":\"Kyeongjun Lee, Hayan Nam\",\"doi\":\"10.1142/s1793042124500891\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Finding the Frobenius number and the genus of any numerical semigroup <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>S</mi></math></span><span></span> 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.</p>\",\"PeriodicalId\":14293,\"journal\":{\"name\":\"International Journal of Number Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793042124500891\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793042124500891","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
求任何数值半群 S 的弗罗贝尼斯数和属是一个众所周知的公开问题。同样，如何表达数值半群的商的弗罗贝尼斯数和属也是一个研究课题。本文通过枚举各类数字半群的希尔伯特数列，展示了由以下数列之一生成的数字半群商的属数表达式：算术级数、几何级数和毕达哥拉斯三重数。
The genus of a quotient of several types of numerical semigroups
Finding the Frobenius number and the genus of any numerical semigroup 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.
期刊介绍：
This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
