DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY

Abstract

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for establishing the symmetry and Schur positivity of quasisymmetric functions.

Keywords

• 05E05 (primary)
• 05A30
• 05E10 (secondary)