How to Extend Karolyi and Nagy's BRILLIANT Proof of the Zeilberger-Bressoud q-Dyson Theorem in order to Evaluate ANY Coefficient of the q-Dyson Product

2013/08/13 by Ekhad, Shalosh B., Zeilberger, Doron
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1308.2983

Abstract

We show how to extend the Karolyi-Nagy beautiful proof of the Zeilberger-Bressoud q-Dyson theorem, (first proved by Zeilberger and Bressoud in 1985, and originally conjectured by George Andrews in 1975), that states that the constant term of a certain Laurent polynomial equals the q-multinomial coefficient, how to evaluate any other specific coefficient. The algorithm implies that any such coefficient is always a certain rational function (that the algorithm finds) times the q-multinomial coefficient.

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