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A determinant-like formula for the Kostka numbers

2005/01/10 by Mathias Lederer, Lederer, Mathias
Mathematics · #05A10 (Primary) 20C30 (Secondary) #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #math.CO #math.RT #msc:05A10 #msc:05A15 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0501132

12 pages

openalex publication_date 2005/01/10 · arxiv created 2005/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Young tableaux are ubiquitous in various branches of mathematics. There are two counting formulas for standard Young tableaux. The first involves a determinant and goes back to Frobenius and Young, and the second is the hook formula by Frame, Robinson and Thrall. We present a generalization of the determinant formula for semistandard Young tableaux of given shape and of given content. Our counting formula -- though not a determinant -- is a generalization of the determinant formula by Frobenius and Young.

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