2024/04/28 by Benjamin Dequêne, Dequêne, Benjamin
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2404.18215
The classical Robinson--Schensted--Knuth correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableaux. Based on the work of, among others, Burge, Hillman, Grassl, Knuth and Gansner, it is known that a version of this correspondence gives, for any nonzero integer partition λ, a bijection from arbitrary fillings of λ to reverse plane partitions of shape λ, via Greene--Kleitman invariants. By bringing out the combinatorial aspects of our recent results on quiver representations, we construct a family of bijections from fillings of λ to reverse plane partitions of shape λ parametrized by a choice of Coxeter element in a suitable symmetric group. We recover the above version of the Robinson--Schensted--Knuth correspondence for a particular choice of Coxeter element depending on λ.