Two families of constant term identities

In 1985, Bressoud and Goulden derived the formula for the constant term in ∏ ( i , j ) ∈ T x j x i ∏ 0 ≤ i < j ≤ n ( x i x j ) a i ( q x j x i ) a j - 1 , where T ⊆ { ( i , j ) ∣ 0 ≤ i < j ≤ n } . This result implies the Andrews’ q -Dyson identity. In 2006, Gessel and Xin proved the q -Dyson i...

Full description

Saved in:
Bibliographic Details
Published inThe Ramanujan journal Vol. 58; no. 3; pp. 701 - 722
Main Author Zhou, Keru
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2022
Springer Nature B.V
Subjects
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Polynomials
Series
Constant term
Dyson style product
05A30
Tournament
Laurent series
Online AccessGet full text

Cover

More Information
Summary:In 1985, Bressoud and Goulden derived the formula for the constant term in ∏ ( i , j ) ∈ T x j x i ∏ 0 ≤ i < j ≤ n ( x i x j ) a i ( q x j x i ) a j - 1 , where T ⊆ { ( i , j ) ∣ 0 ≤ i < j ≤ n } . This result implies the Andrews’ q -Dyson identity. In 2006, Gessel and Xin proved the q -Dyson identity by considering both sides of the equality as polynomials in q a 0 . We use this approach to determine the coefficients of x 0 / x 1 and x 0 / x 2 in Laurent polynomials studied by Bressoud and Goulden.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-022-00569-1