Abstract:Let $\lambda=(\lambda_1 \geqslant \ldots \geqslant \lambda_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{\lambda_1+k-1}$, we construct a bijection from fillings of $\lambda$ to reverse plane partitions. We recover two previous generalizations of the Robinson--Schensted--Knuth correspondence for particular choices of Coxeter element depending on $\lambda$: 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 $A_{\lambda_1+k}$ quivers.
From: Benjalmin Dequêne [view email]
[v1]
Thu, 18 Jul 2024 15:23:03 UTC (50 KB)
[v2]
Tue, 17 Dec 2024 08:15:32 UTC (58 KB)
[v3]
Tue, 8 Sep 2026 14:51:40 UTC (52 KB)
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