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.
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