2016/01/05 by William J. Keith, Keith, William J.
Mathematics · #05A17 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A17
paper · pdf · doi:10.48550/arxiv.1601.00926
Presented at the Kliakhandler Conference 2015, Algebraic Combinatorics and Applications, at Michigan Technological University. To appear in the Proceedings
arxiv created 2016/01/05 · arxiv updated 2016/01/06
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 on the mock theta functions. Throughout, we state a number of observations and questions that can motivate an array of investigations.