A proof of Andrews' q-Dyson conjecture

Doron Zeilberger; David M. Bressoud

doi:10.1016/0012-365X(85)90081-0

A proof of Andrews' q-Dyson conjecture

Doron Zeilberger, David M. Bressoud

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Abstract

Let (y)_a=(1-y)(1-qy)...(1-q^a-1y). We prove that the constant term of the Laurent polynomial Π_1≤i<j≤n(x_i/x_j)a_i(qx_j/x_i)_{a_j}, where x₁,...,x_n, q are commmuting indeterminates and a₁,...,a_n are non-negative integers, equals (q)_a₁+...+a_n/(q)_{a_n}. This settles in the affirmative a conjecture of George Andrews (in: R.A. Askey, ed., Theory and Applications of Special Functions, Academic Press, New York, 1975, 191-224].

Original language	English (US)
Pages (from-to)	201-224
Number of pages	24
Journal	Discrete Mathematics
Volume	54
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(85)90081-0
State	Published - Apr 1985
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(85)90081-0

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title = "A proof of Andrews' q-Dyson conjecture",

abstract = "Let (y)a=(1-y)(1-qy)...(1-qa-1y). We prove that the constant term of the Laurent polynomial Π1≤i(xi/xj)ai (qxj/xi)aj, where x1,...,xn, q are commmuting indeterminates and a1,...,an are non-negative integers, equals (q)a1+...+an/(q)an . This settles in the affirmative a conjecture of George Andrews (in: R.A. Askey, ed., Theory and Applications of Special Functions, Academic Press, New York, 1975, 191-224].",

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AU - Bressoud, David M.

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N2 - Let (y)a=(1-y)(1-qy)...(1-qa-1y). We prove that the constant term of the Laurent polynomial Π1≤i(xi/xj)ai (qxj/xi)aj, where x1,...,xn, q are commmuting indeterminates and a1,...,an are non-negative integers, equals (q)a1+...+an/(q)an . This settles in the affirmative a conjecture of George Andrews (in: R.A. Askey, ed., Theory and Applications of Special Functions, Academic Press, New York, 1975, 191-224].

AB - Let (y)a=(1-y)(1-qy)...(1-qa-1y). We prove that the constant term of the Laurent polynomial Π1≤i(xi/xj)ai (qxj/xi)aj, where x1,...,xn, q are commmuting indeterminates and a1,...,an are non-negative integers, equals (q)a1+...+an/(q)an . This settles in the affirmative a conjecture of George Andrews (in: R.A. Askey, ed., Theory and Applications of Special Functions, Academic Press, New York, 1975, 191-224].

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A proof of Andrews' q-Dyson conjecture

Abstract

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