Young classes of permutations
Combinatorics
2012-04-19 v4
Abstract
We characterise those classes of permutations having the property that for every tableau shape either every permutation of that shape or no permutation of that shape belongs to the class. The characterisation is in terms of the dominance order for partitions (and their conjugates) and shows that for any such class there is a constant k such that no permutation in the class can contain both an increasing and a decreasing sequence of length k.
Keywords
Cite
@article{arxiv.1008.4615,
title = {Young classes of permutations},
author = {Michael Albert},
journal= {arXiv preprint arXiv:1008.4615},
year = {2012}
}
Comments
11 pages, this is the final version as accepted by the Australasian Journal of Combinatorics. Some more minor typos have been corrected