Formula:8647

Digital Library of Mathematical Functions ID 26.14.E3

${\displaystyle{\displaystyle\sum_{\sigma\in\mathfrak{S}_{n}}q^{\mathop{\mathrm{inv}}(\sigma)}=\sum_{\sigma\in\mathfrak{S}_{n}}q^{\mathop{\mathrm{maj}}(\sigma)}=\prod_{j=1}^{n}\frac{1-q^{j}}{1-q}.}}$

Symbols List

• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathfrak{S}_{\NVar{n}}}}$: set of permutations of { 1 , 2 , … , n }
• ${\displaystyle{\displaystyle j}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: parameter
 

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