奇异分拆上Schur恒等式的一个细分OA
A Refinement of Schur's Identity on Partitions into Distinct Odd Parts
Schur 建立如下分拆恒等式:正整数 n 的各部分为奇数且互异的分拆数目等于正整数 n 的各部分均不模4 余2,任意两部分至少相差4 且无连续的4 的倍数的分拆数目.本文证明前一类分拆的长度与后一类分拆的加权长度(每个被4 整除的部分计算两次)是同分布的,从而得到 Schur 分拆恒等式的一个细分.
Schur established the following partition identity:the number of par-titions of n into distinct odd parts is the same as the number of partitions of n where each part is not congruent to 2 modulo 4,any two parts differ by at least 4,and no consecutive multiples of 4 appear.In this paper,we prove that the length of the first type of partitions is equidistributed with the weighted length(partitons divisible by 4 is counted twice)of the second type of partitions,which implies a refinement of Schur's result.
刘晗;林丽双
集美大学理学院,福建 厦门 361021集美大学理学院,福建 厦门 361021
数理科学
分拆奇异分拆Schur恒等式
partitionsdistinct odd partitionsSchur's identity
《集美大学学报（自然科学版）》 2026 (3)
358-362,5
国家自然科学基金面上项目(11871246)
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