Variations of Andrews-Beck type congruences

preprint2020arXivOpen access

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.

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Variations of Andrews-Beck type congruences

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