Combinatorial proofs of hook generating functions for skew plane partitions

Abstract

We provide combinatorial proofs of two hook generating functions for skew plane partitions. One proof involves the Hillman-Grassl (1976) algorithm and the other uses a modification of Schützenberger's (1963, 1977) “jeu de taquin” due to Kadell (to appear). We also provide a bijection showing directly that these two generating functions are equal. Analogous results for skew shifted plane partitions are proved. Finally, some open questions are discussed.