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DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY

Part of: Algebraic combinatorics Combinatorics

Published online by Cambridge University Press:  22 July 2015

SAMI H. ASSAF
SAMI H. ASSAF*
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA; shassaf@usc.edu

Abstract

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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.

MSC classification

Primary: 05E05: Symmetric functions and generalizations
Secondary: 05A30: $q$-calculus and related topics 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 3 , 2015 , e12
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2015

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