Variations of Andrews-Beck type congruences

Song Heng Chan; Renrong Mao; Robert Osburn

doi:10.1016/j.jmaa.2020.124771

paper

Variations of Andrews-Beck type congruences

arXiv:2005.01272 · doi:10.1016/j.jmaa.2020.124771

Abstract

We prove three variations of recent results due to Andrews on congruences for $N T (m, k, n)$ , the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$ . We also conjecture new congruences and relations for $N T (m, k, n)$ and for a related crank-type function.

15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Applications