Bender-Knuth involutions on linear extensions of posets

2023/02/24 by Judy Hsin-Hui Chiang, Anh Trong Nam Hoang, Chiang, Judy Hsin-Hui +11 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2302.12425

Abstract

We study the permutation group BK_P generated by Bender-Knuth moves on linear extensions of a poset P, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets P for which the cactus relations hold in BK_P. We also examine BK_P as a subgroup of the symmetric group \mathfrakS_L(P) on the set of linear extensions of P with the focus on analyzing posets P for which BK_P = \mathfrakS_L(P).

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• Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity

Related

• Shifted Bender-Knuth moves and a shifted Berenstein-Kirillov group
• The Berenstein-Kirillov group and cactus groups
• A shifted Berenstein-Kirillov group and the cactus group
• The Cactus Group Property for Ordinal Sums of Disjoint Unions of Chains
• Inverse limits of various posets