On principal hook length partitions and durfee sizes in skew characters
Combinatorics
2011-03-24 v2 Representation Theory
Abstract
In this paper we construct for a given arbitrary skew diagram A all partitions nu with maximal principal hook lengths among all partitions with the character [nu] appearing in the skew character [A]. Furthermore we show that these are also partitions with minimal Durfee size. This we use to give the maximal Durfee size for [nu] appearing in [A] for the cases when A decays into two partitions and for some special cases of A. Also this gives conditions for two skew diagrams to represent the same skew character.
Cite
@article{arxiv.0802.0417,
title = {On principal hook length partitions and durfee sizes in skew characters},
author = {Christian Gutschwager},
journal= {arXiv preprint arXiv:0802.0417},
year = {2011}
}
Comments
13 pages, minor changes from v1 to v2 as suggested by the referee, to appear in Annals. Comb