The part-frequency matrices of a partition

William J. Keith
2016 Journal of Algebra Combinatorics Discrete Structures and Applications  
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]
more » ... 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.
doi:10.13069/jacodesmath.41075 fatcat:vxg5sghc2fcsnjms3optkqnwhe