A proof of Andrews’ q-Dyson conjecture
2006; Elsevier BV; Volume: 306; Issue: 10-11 Linguagem: Inglês
10.1016/j.disc.2006.03.023
ISSN1872-681X
AutoresDoron Zeilberger, David M. Bressoud,
Tópico(s)Analytic Number Theory Research
ResumoLet (y)a=(1-y)(1-qy)⋯(1-qa-1y). We prove that the constant term of the Laurent polynomial ∏1⩽i<j⩽n(xi/xj)ai(qxj/xi)aj, where x1,…,xn,q are commuting indeterminates and a1,…,an are non-negative integers, equals (q)a1+⋯+an/(q)a1…(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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