The part-frequency matrices of a partition

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.