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On Principal Hook Length Partitions and Durfee Sizes in Skew Characters
Christian Gutschwager
Institut f¨ur Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universit¨at Hannover, Welfengarten 1, Hannover D-30167, German
Annals of Combinatorics 15 (1) pp.81-94 January, 2011
AMS Subject Classification: 05E05, 05E10, 14M15, 20C30
We construct for a given arbitrary skew diagram A all partitions v with maximal principal hook lengths among all partitions with [v] 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 [v] 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.
Keywords: principal hook lengths, Durfee size, skew characters, symmetric group, skew Schur functions, Schubert Calculus


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