Séminaire Lotharingien de Combinatoire, 91B.76 (2024), 12 pp.
Benjamin Dequêne
An Extended Generalization of RSK via The Combinatorics of Type A Quiver Representations
Abstract.
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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