New Relations of the mex with other partition statistics

When/Where:

March 1, 2022, 1:55 — 2:45 pm at LIT 368.

Abstract:

In a recent pioneering work, Andrews and Newman defined an extended function \(p_{A,a}(n)\) of their minimal excludant or “mex” of a partition function and by considering the cases \(p_{k,k}(n)\) and \(p_{2k,k}(n)\), they unearthed connections to the rank and crank of partitions and some restricted partitions. In this work, we generalize their results and associate the extended mex function to the number of partitions of an integer with arbitrary bound on the rank and crank. We also derive a new result expressing the smallest parts function of Andrews as a finite sum of this extended mex function. We obtain some more restricted partition identities as well.

This is joint work with Avi Mukhopadhyay and Rishabh Sarma.