On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

摘要

We construct for a given arbitrary skew diagram A all partitions ν with maximal principal hook lengths among all partitions with [ν] appearing in A. Furthermore, we show that these are also partitions with minimal Durfee size. We use this to give the maximal Durfee size for [ν] appearing in A for the cases when A decays into two partitions and for some special cases of A. We also deduce necessary conditions for two skew diagrams to represent the same skew character.