l-近正规划线分拆对函数同余性质的组合研究  

Combinatorial Studies on Congruence Properties for Almost l-regular Overpartition Pairs Functions

作　　者：郝小健 HAO Xiaojian(College of Science and Mathematics,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院数理学院,江苏南京211167

出　　处：《山西大学学报（自然科学版）》2023年第4期762-770,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12101307)。

摘　　要：对整数分拆理论的研究通常采用代数方法与组合方法,其中组合方法由于其优美的构造受到学者们的青睐。建立统计量将分拆集合划分为等势的剩余类从而组合解释分拆函数的Ramanujan型同余性质是组合方法在分拆理论中的重要应用之一。近期,Ballantine和Merca考察了l-近正规划线分拆,并且给出了3-近正规划线分拆函数所满足的同余性质。然而3-近正规划线分拆函数并不满足模3的Ramanujan型同余性质,因此本文考察l-近正规划线分拆对,通过建立双射构造分拆统计量Ar_(l)-秩对任意l≡0(mod 3)组合解释了l-近正规划线分拆对函数所满足的Ramanujan型同余性质。此外,对于l=3,本文给出了无穷系族同余性质的组合解释。Studies on the theory of integer partition usually adopt algebraic and combinatorial methods, and the latter attracts significant attention due to its beautiful construction. Investigating the Ramanujan-type congruence properties for partition functions by constructing statistics to group the set of partitions into equivalent subsets is one of the important applications of combinatorial methods in the theory of integer partition. Recently, Ballantine and Merca have studied the almost l-regular overpartitions, and gave a congruence property for l=3. However, the almost 3-regular overpartitions function does not satisfy a Ramanujan-type congruence property modulo 3. In this paper, we introduce the Ar_(l)-rank of almost l-regular overpartition pairs by constructing a bijection to give combinatorial interpretations for Ramanujan-type congruence properties for the partition functions of l-regular overpartition pairs with l≡0 mod 3. Moreover, we provide combinatorial interpretations for infinite families of congruence properties for l=3.

关 键 词：分拆统计量 组合解释 双射 同余 

分 类 号：O157.2[理学—数学]