English

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.

Keywords

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

R2 v1 2026-06-22T00:26:24.803Z