The Schur Expansion of Macdonald Polynomials
نویسنده
چکیده
Building on Haglund’s combinatorial formula for the transformed Macdonald polynomials, we provide a purely combinatorial proof of Macdonald positivity using dual equivalence graphs and give a combinatorial formula for the coefficients in the Schur expansion.
منابع مشابه
Dual equivalence graphs, ribbon tableaux and Macdonald polynomials
We make a systematic study of a new combinatorial construction called a dual equivalence graph. Motivated by the dual equivalence relation on standard Young tableaux introduced by Haiman, we axiomatize such constructions and prove that the generating functions of these graphs are Schur positive. We construct a graph on k-ribbon tableaux which we conjecture to be a dual equivalence graph, and we...
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متن کاملSynopsis: Dual Equivalence Graphs, Ribbon Tableaux and Macdonald Polynomials
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 M...
متن کاملDual Equivalence Graphs and a Combinatorial Proof of Llt and Macdonald Positivity
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. By constructing a graph on ribbon tableaux which we transform into a dual equivalence graph, we give a combinatorial proof of the symmetry and Schur positivity of the ribbon tableaux generating func...
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تاریخ انتشار 2007