An extended generalization of RSK correspondence via A type quiver representations

Let λ=(λ₁ … λₖ > 0). For any c Coxeter element of Sλ₁+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 Aλ₁+k quivers.