Variations of Andrews-Beck type congruences

Abstract

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$, 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 $NT(m,k,n)$ and for a related crank-type function.

arXiv comment15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Applications

References in corpus (4)

• Rank and crank moments for overpartitions
• M_2-rank differences for partitions without repeated odd parts
• M_2-rank differences for overpartitions
• Two Families of Buffered Frobenius Representations of Overpartitions

Cited by in corpus (1)

• Partitions with parts separated by parity: conjugation, congruences and the mock theta functions