A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin
The author gives a bijective proof of the product formula for the principal specialization of super Schur functions (also called hook Schur functions) using the combinatorial description of super Schur functions in terms of certain tableaux due to Berele and Regev [cf. \textit{A. Berele} and \textit{A. Regev}, Hook Young diagrams with applications to combinatorics and representations of Lie superalgebras, Adv. Math. 44, 118-175 (1987; Zbl 0617.17002)]. His bijective proof is based on the Hillman-Grassl algorithm [cf. \textit{A. P. Hillman} and \textit{R. M. Grassl}, Reverse plane partitions and tableau hook numbers, J. Comb. Theory, Ser. A 21, 216-221 (1976; Zbl 0341.05008)] and a modified version of Schützenberger's jeu de taquin. He then explores the relationship between his modified jeu de taquin and a modified jeu de taquin by \textit{I. Goulden} and \textit{C. Green} [A new tableau representation for supersymmetric Schur functions, J. Algebra 170, No. 2, 687-703 (1994; Zbl 0840.20008)]. He defines a common extension and proves an invariance property for it, thus discovering that both modified jeu de taquins are, though different, equivalent.
scientific article; zbMATH DE number 907653