The part-frequency matrices of a partition

• Main Author: William J. Keith
• Format: Article
• Language: English
• Published: Yildiz Technical University 2016-09-01
• Series: Journal of Algebra Combinatorics Discrete Structures and Applications
• Online Access: http://dergipark.ulakbim.gov.tr/jacodesmath/article/view/5000198243

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