Eulerian polynomials and the g-indices of Young tableaux.

In this paper, we introduce k-Young tableaux and their g-indices. We first present certain expansions of (c(x)D)^n in terms of inversion sequences as well as k-Young tableaux, where c(x) is a smooth function in the indeterminate x and D is the derivative with respect to x. By studying the connections between k-Young tableaux and standard Young tableaux, we then present combinatorial interpretations of Eulerian polynomials, second-order Eulerian polynomials, and André polynomials in terms of standard Young tableaux. [ABSTRACT FROM AUTHOR]