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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.01272
- arXiv:
- arXiv:2005.01272
- Bibcode:
- 2020arXiv200501272C
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Combinatorics;
- 11P81;
- 05A17
- E-Print:
- 15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Applications