Geodesic
DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY
Forum of Mathematics, Sigma, Tome 3 (2015)

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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. 
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     author = {SAMI H. ASSAF},
     title = {DUAL {EQUIVALENCE} {GRAPHS} {I:} {A} {NEW} {PARADIGM} {FOR} {SCHUR} {POSITIVITY}},
     journal = {Forum of Mathematics, Sigma},
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SAMI H. ASSAF. DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2015.15

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