论文标题
$ p $ - 数字的半群，带有$ p $ - 对称属性
$p$-numerical semigroups with $p$-symmetric properties
论文作者
论文摘要
Frobenius的著名线性借离问题中所谓的Frobenius编号是最大的整数，因此线性方程$ a_1 x_1+\ cdots+cdots+a_k x_k = n $（$ a_1，\ dots，\ dots，a_k $ a_k $ a_k $均给予带有$ \ gcd的正整数（整数解决方案$（x_1，\ dots，x_k）$。广义的Frobenius编号（称为$ P $ -FROBENIUS编号）是最大的整数，因此该线性方程最多具有$ P $ Solutions。也就是说，当$ p = 0 $时，$ 0 $ -FROBENIUS编号是原始的Frobenius编号。 在本文中，我们通过基于表示数量的数量来开发数字半群理论的概括来介绍和讨论$ p $ numerical的半群。也就是说，对于某些非阴性整数$ P $，$ p $ - gaps，$ p $ - 超对称的半群，$ p $ -pseudo-pseudo-ymmetric-metmemmetric semigroups等，类似程序是定义的，并获得了它们的属性。当$ p = 0 $时，它们分别对应于原始差距，对称的半群和伪对称的半群。
The so-called Frobenius number in the famous linear Diophantine problem of Frobenius is the largest integer such that the linear equation $a_1 x_1+\cdots+a_k x_k=n$ ($a_1,\dots,a_k$ are given positive integers with $\gcd(a_1,\dots,a_k)=1$) does not have a non-negative integer solution $(x_1,\dots,x_k)$. The generalized Frobenius number (called the $p$-Frobenius number) is the largest integer such that this linear equation has at most $p$ solutions. That is, when $p=0$, the $0$-Frobenius number is the original Frobenius number. In this paper, we introduce and discuss $p$-numerical semigroups by developing a generalization of the theory of numerical semigroups based on this flow of the number of representations. That is, for a certain non-negative integer $p$, $p$-gaps, $p$-symmetric semigroups, $p$-pseudo-symmetric semigroups, and the like are defined, and their properties are obtained. When $p=0$, they correspond to the original gaps, symmetric semigroups, and pseudo-symmetric semigroups, respectively.
