A $q$-polynomial identity
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- by Kung-Wei Yang PDF
- Proc. Amer. Math. Soc. 95 (1985), 152-154 Request permission
Abstract:
We show that the $q$-polynomial coefficients $[_{\;r}^{n \cdot m}]$ (see the definition preceding Theorem 1), which are the generating functions of the number of inversions between multisets, satisfy the beautiful identity \[ \prod \limits _{i = 1}^n {\left ( {\sum \limits _{j = 0}^m {{q^{jm(i - 1) + (_2^j)}}{t^j}} } \right ) = \sum \limits _{r = 0}^{nm} {[_{\;r}^{n \cdot m}} ]{q^{(_2^r)}}{t^r}} .\]References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 152-154
- MSC: Primary 05A15; Secondary 05A30
- DOI: https://doi.org/10.1090/S0002-9939-1985-0796465-8
- MathSciNet review: 796465