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.

24 pages, 27 figures, to appear in Forum of Mathematics, Sigma. arXiv admin note: substantial text overlap with arXiv:1005.3759

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