论文标题
与数值半群相关的对称多项式
Symmetric polynomials associated with numerical semigroups
论文作者
论文摘要
我们研究了一种新型的对称多项式P_N（x_1，...，...，x_m），在m真实变量中，该度n在数值半群中出现了。我们建立了他们的基本属性，并通过功率总和e_k = \ sum_ {j = 1}^m x_j^k找到其表示形式。 We observe a visual similarity between normalized polynomials P_n(x_1,...,x_m)/χ_m, where χ_m=\prod_{j=1}^m x_j, and a polynomial part of a partition function W(s,{d_1,...,d_m}), which gives a number of partitions of s\ge 0 into m positive integers d_j, and put forward a猜想他们的关系。
We study a new kind of symmetric polynomials P_n(x_1,...,x_m) of degree n in m real variables, which have arisen in the theory of numerical semigroups. We establish their basic properties and find their representation through the power sums E_k=\sum_{j=1}^m x_j^k. We observe a visual similarity between normalized polynomials P_n(x_1,...,x_m)/χ_m, where χ_m=\prod_{j=1}^m x_j, and a polynomial part of a partition function W(s,{d_1,...,d_m}), which gives a number of partitions of s\ge 0 into m positive integers d_j, and put forward a conjecture about their relationship.
