论文标题
两个持续定期身份的家庭
Two Families of Constant Term Identities
论文作者
论文摘要
1985年，Bressoud和Goulden在$ \ prod _ {（i，j）\ in t} \ frac {x_j} {x_i} {x_i} \\\\\\\\\\\\\\\ prod_ {0 \ le i <j \ le le i <j \ le <j \ le <j \ le n}（\ frac {x_i} {x_j}）_ {a_i}（\ frac {qx_j} {x_i}）_ {a_j-1} $，其中$ t \ subseteq \ subseteq \ {（i，j）这个结果意味着安德鲁斯的$ q $ -Dyson身份。在2006年，Gessel和Xin通过将平等的双方视为$ q^{a_0} $中的多项式，证明了$ q $ -Dyson的身份。我们使用这种方法来确定Bressoud和Goulden研究的laurent多项式的$ x_0/x_1 $和$ x_0/x_2 $的系数。
In 1985, Bressoud and Goulden derived the formula for the constant term in $\prod_{(i,j)\in T} \frac{x_j}{x_i}\\\prod_{0\le i<j \le n}(\frac{x_i}{x_j})_{a_i}(\frac{qx_j}{x_i})_{a_j-1}$, where $T \subseteq \{(i,j)\mid 0\le i<j \le n\}$. 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.
