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- Title
The part-frequency matrices of a partition.
- Authors
Keith, William J.
- Abstract
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.
- Subjects
MATRICES (Mathematics); MATHEMATICAL sequences; PARTITIONS (Mathematics); THETA functions; GENERALIZABILITY theory
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2017, Vol 4, Issue 3, p177
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.41075