集美大学学报（自然科学版）2026，Vol.31Issue(3)：358-362,5.DOI:10.19715/j.jmuzr.2026.03.09
奇异分拆上Schur恒等式的一个细分
A Refinement of Schur's Identity on Partitions into Distinct Odd Parts
摘要
Abstract
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.关键词
分拆/奇异分拆/Schur恒等式Key words
partitions/distinct odd partitions/Schur's identity分类
数理科学引用本文复制引用
刘晗,林丽双..奇异分拆上Schur恒等式的一个细分[J].集美大学学报（自然科学版）,2026,31(3):358-362,5.基金项目
国家自然科学基金面上项目(11871246) （11871246）
