P-Frobenius问题与p-对称数值半群
P-Frobenius problem and p-symmetric numerical semigroup
应皓天 1小松尚夫1
作者信息
- 1. 浙江理工大学理学院,杭州 310018
- 折叠
摘要
针对p-Frobenius问题中出现的非对称性问题,利用数值半群理论以及Apery集等工具研究了p-Frobenius问题对应的p-对称数值半群.首先利用数值半群和Apery集等工具对p-Frobenius问题进行预处理,得到了对应数值半群和Apery集的各个变量;并将这些变量与对称数值半群和Frobenius问题进行对比,由此定义了p-对称数值半群,并给出了 p-对称性的刻画.在此基础上,首先给出了两大类p-对称数值半群,其次研究了对称数值半群与p-对称数值半群的p化关联性.这两类p-对称数值半群给出了大量具体实例,而p化关联性则可用于处理p-Frobenius问题中出现的非对称问题.
Abstract
In order to deal with the non-symmetry in p-Frobenius problem,we use the theory of numerical semigroup and Apery set to research the corresponding p-symmetric numerical semigroup.We first use the numerical semigroup and the Apery set as tools to get all kinds of variables of the p-Frobenius problem in advance,then we compare these results with the symmetric numerical semigroup and Frobenius problem.Then we can define the p-symmetric numerical semigroup and obtain its properties.On the base of these properties,we find two kinds ofp-symmetric numerical semigroup and then research the relationship between the symmetric numerical semigroup and the p-symmetric numerical semigroup.These two kinds of p-symmetric numerical semigroups give lots of examples and the properties can do help to research the non-symmetry in p-Frobenius problem.
关键词
数值半群/线性丢番图方程/Apery集/对称性/Frobenius问题Key words
numeical semigroup/linear Diophantine equation/Apery set/symmetry/Frobenius problem引用本文复制引用
出版年
2024
NETL
NSTL
万方数据