An extended generalization of RSK correspondence via A type quiver representations

2024/07/18 by Benjamin Dequêne, Dequêne, Benjamin
Mathematics · Computer Science · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2407.13581

Abstract

Let λ=(λ₁ \geqslant … \geqslant λ_k > 0). For any c Coxeter element of \mathfrakS_λ1+k-1, we construct a bijection from fillings of λ to reverse plane partitions. We recover two previous generalizations of the Robinson--Schensted--Knuth correspondence for particular choices of Coxeter element depending on λ: one based on the work of, among others, Burge, Hillman, Grassl, Knuth, and uniformly presented by Gansner; the other developed by Garver, Partrias, and Thomas, and independently by Dauvergne, called Scrambled RSK. Our results in this paper develop the combinatorial consequence of our previous work of type A_λ1+k quivers.

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