Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics
An Extended Generalization of RSK Correspondence via A Type Quiver Representations
Abstract
Let λ=(λ1 geqslant … geqslant λk > 0). For any c Coxeter element of Sλ1+k, 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 Aλ1+k−1 quivers.
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BibTeX
@article{dequene2026extended,
title = {{An Extended Generalization of RSK Correspondence via $A$ Type Quiver Representations}},
author = {Benjamin Dequene},
journal = {The Electronic Journal of Combinatorics},
year = {2026},
month = nov,
doi = {10.37236/15236},
url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p30},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - An Extended Generalization of RSK Correspondence via A Type Quiver Representations
AU - Benjamin Dequene
PY - 2026
DA - 2026/11/06
JO - The Electronic Journal of Combinatorics
DO - 10.37236/15236
UR - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p30
AB - Let λ=(λ_1 geqslant … geqslant λ_k > 0). For any c Coxeter element of S_λ_1+k, 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_λ_1+k−1 quivers.
SN - 1077-8926
ER -