The part-frequency matrices of a partition

Journal of Algebra Combinatorics Discrete Structures and Applications

article

William J. Keith¹ 

[1] Department of Mathematics, Michigan Tech University

关键词: Partitions;    Partition rank;    Glaisher’s bijection;   

DOI  :  10.13069/jacodesmath.41075

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher’s bijection. We prove results that suggest surprising usefulness for such a simple tool, including the existence of a related statistic that realizes every possible Ramanujan-type congruence for the partition function. To further exhibit its research utility, we give an easy generalization of a theorem of Andrews, Dixit and Yee [1] on the mock theta functions. Throughout, we state a number of observations and questions that can motivate an array of investigations.

【 授权许可】

CC BY