The t-core of an s-core
Combinatorics
2012-02-20 v2
Abstract
We consider the -core of an -core partition, when and are coprime positive integers. Olsson has shown that the -core of an -core is again an -core, and we examine certain actions of the affine symmetric group on -cores which preserve the -core of an -core. Along the way, we give a new proof of Olsson's result. We also give a new proof of a result of Vandehey, showing that there is a simultaneous - and -core which contains all others.
Cite
@article{arxiv.1007.1071,
title = {The t-core of an s-core},
author = {Matthew Fayers},
journal= {arXiv preprint arXiv:1007.1071},
year = {2012}
}