On principal hook length partitions and durfee sizes in skew characters

Details On principal hook length partitions and durfee sizes in skew characters On principal hook length partitions and durfee sizes in skew characters

2008-02-04

arxiv.org/abs/0802.0417v2

Mathematics

Combinatorics

13 pages, minor changes from v1 to v2 as suggested by the referee, to appear in Annals. Comb

Scientific paper

10.1007/s00026-011-0084-7

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.

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