A proof of Andrews' -Dyson conjecture for

Author:
Kevin W. J. Kadell

Journal:
Trans. Amer. Math. Soc. **290** (1985), 127-144

MSC:
Primary 33A15; Secondary 05A30

DOI:
https://doi.org/10.1090/S0002-9947-1985-0787958-2

MathSciNet review:
787958

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Abstract: Andrews' -Dyson conjecture is that the constant term in a polynomial associated with the root system is equal to the -multinomial coefficient. Good used an identity to establish the case , which was originally raised by Dyson. Andrews established his conjecture for and Macdonald proved it when or for all . We use a -analog of Good's identity which involves a remainder term and linear algebra to establish the conjecture for . The remainder term arises because of an essential problem with the -Dyson conjecture: the symmetry of the constant term. We give a number of conjectures related to the symmetry.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0787958-2

Article copyright:
© Copyright 1985
American Mathematical Society