Skew Gelfand-Tsetlin Patterns, Lattice Permutations, and Skew Pattern Polynomials

A modification of the well-known Gelfand-Tsetlin patterns, which are one-to-one with Young-Weyl semistandard tableaux is introduced. These new patterns are in one-to-one correspondence with skew-tableaux, and with a slight modification can be used to enumerate lattice permutations. In particular, the coupling rule for angular momentum takes an elementary form in terms of these modified patterns. These interrelations will be presented, together with an outline of the construction of a class of polynomials that generalize the skew Schur functions.