On Principal Hook Length Partitions and Durfee Sizes in Skew Characters

被引：0

作者：

Gutschwager, Christian ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany

来源：

ANNALS OF COMBINATORICS | 2011年 / 15卷 / 01期

关键词：

principal hook lengths; Durfee size; skew characters; symmetric group; skew Schur functions; Schubert Calculus; SCHUR-FUNCTIONS;

D O I：

10.1007/s00026-011-0084-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct for a given arbitrary skew diagram A all partitions. with maximal principal hook lengths among all partitions with [nu] 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 [nu] 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.

引用

页码：81 / 94

页数：14

共 14 条

[1] On Principal Hook Length Partitions and Durfee Sizes in Skew Characters
Christian Gutschwager
Annals of Combinatorics, 2011, 15 : 81 - 94
[2] On base partitions and cover partitions of skew characters
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ELECTRONIC JOURNAL OF COMBINATORICS, 2008, 15 (01):
[3] Hook length and symplectic content in partitions
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JOURNAL OF COMBINATORIAL THEORY SERIES A, 2023, 200
[4] Partitions with fixed largest hook length
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[5] Partitions with fixed largest hook length
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[6] Symmetry distribution between hook length and part length for partitions
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DISCRETE MATHEMATICS, 2009, 309 (20) : 6070 - 6073
[7] An involution for symmetry of hook length and part length of pointed partitions
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DISCRETE MATHEMATICS, 2010, 310 (10-11) : 1633 - 1639
[8] COMBINATORIAL PROOFS OF HOOK GENERATING-FUNCTIONS FOR SKEW PLANE PARTITIONS
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[9] Hook length biases in ordinary and t-regular partitions
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JOURNAL OF NUMBER THEORY, 2024, 264 : 41 - 58
[10] Hook, line and sinker: A bijective proof of the skew shifted hook-length formula
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EUROPEAN JOURNAL OF COMBINATORICS, 2020, 86

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