SYNOPSIS: DUAL EQUIVALENCE GRAPHS, RIBBON TABLEAUX AND MACDONALD POLYNOMIALS

Abstract

The primary focus of this dissertation is symmetric function theory. The main objectives are to present a new combinatorial construction which may be used to establish the symmetry and Schur positivity of a function expressed in terms of monomials, and to use this method to find a combinatorial description of the Schur expansion for two important classes of symmetric functions, namely LLT and Macdonald polynomials

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