Identities for the number of standard Young tableaux in some (k,ℓ) hooks

2010/03/09 by Amitai Regev, Regev, Amitai · 1 citation
Mathematics · #05C30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C30

paper · pdf · doi:10.48550/arxiv.1003.1835

openalex publication_date 2010/03/09 · arxiv created 2010/03/14 · arxiv updated 2010/03/16 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

Closed formulas are known for S(k,0;n), the number of standard Young tableaux of size n and with at most k parts, where 1≤ k≤ 5. Here we study the analogue problem for S(k,ℓ;n), the number of standard Young tableaux of size n which are contained in the (k,ℓ) hook. We deduce some formulas for the cases k+ℓ≤ 4.

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• Equal knapsack identities between symmetric group character degrees

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• Asymptotics of the number of standard Young tableaux of skew shape
• Product formulas for certain skew tableaux
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• Enumeration of standard Young tableaux of certain truncated shapes
• Enumeration formulas for Young tableaux in a diagonal strip