Congruences for 9-regular partitions modulo 3
Combinatorics
2013-06-07 v2
Abstract
It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4 and 5. A collection of conjectures includes two congruences modulo higher powers of 2 and a large family of "congruences with exceptions" for these and other regular partitions mod 3.
Cite
@article{arxiv.1306.0136,
title = {Congruences for 9-regular partitions modulo 3},
author = {William J. Keith},
journal= {arXiv preprint arXiv:1306.0136},
year = {2013}
}
Comments
7 pages. v2: added citations and proof of one conjecture from a reader. Submitted version