English

A bijection for partitions simultaneously $s$-regular and $t$-distinct

Combinatorics 2022-08-04 v2

Abstract

In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of Glaisher's bijection, the map may be widely useful in other partition combinatorics. A previous conjecture concerning iterations of Glaisher's bijection is given a counterexample.

Keywords

Cite

@article{arxiv.2207.13840,
  title  = {A bijection for partitions simultaneously $s$-regular and $t$-distinct},
  author = {William J. Keith},
  journal= {arXiv preprint arXiv:2207.13840},
  year   = {2022}
}

Comments

v1, 7 pages; v2, 9 pages

R2 v1 2026-06-25T01:17:31.158Z