A note on the Sundaram--Stanley bijection (or, Viennot for up-down\n tableaux)

2021/08/25 by Elijah Bodish, Ben Elias, Bodish, Elijah +5
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2108.11528

openalex publication_date 2021/08/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We give a direct proof of a result of Sundaram and Stanley: that the\ndimension of the space of invariant vectors in a 2k-fold tensor product of\nthe vector representation of mathfraksp_2n equals the number of\n(n+1)-avoiding matchings of 2k points. This can be viewed as an extension\nof Schensted's theorem on longest decreasing subsequences. Our main tool is an\nextension of Viennot's geometric construction to the setting of up-down\ntableaux.\n

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