Year: 2026
Type: preprint
Abstract: The basic hypergeometric series ${}_{n+1}ϕ_{n}$ whose upper and lower parameters are non-negative integer powers of $q$ satisfying a certain constraint can be, after a normalisation, computed as a positive polynomial. We derive three formulas for this polynomial. The first formula is a generalisation of the MacMahon identity in which an infinite binomial series is identified with a normalised generating function of des and maj statistics of multiset permutations. The second formula is a generating function of multiset permutations for the inversion statistic and a generalisation of the statistic mstc. The third formula is a finite sum containing $2n$ $q$-binomial coefficients.
Source: arXiv (Cornell University)
Author: Garbali, Alexandr
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220940573