Mathematics – Combinatorics
Scientific paper
2004-03-03
Mathematics
Combinatorics
12 pages
Scientific paper
Let $n,p,k$ be three positive integers. We prove that the rational fractions of $q$: $${n \brack k}_{q} {}_3\phi_{2} [ . {matrix}q^{1-k},q^{-p},q^{p-n} q,q^{1-n} {matrix}| q;q^{k+1}]\quad\textrm{and}\quad q^{(n-p)p}\qbi{n}{k}{q} {}_3\phi_2[ . {matrix}q^{1-k},q^{-p},q^{p-n} q,q^{1-n} {matrix}|q;q] $$ are polynomials of $q$ with positive integer coefficients. This generalizes a recent result of Lassalle (Ann. Comb. 6(2002), no. 3-4, 399-405), in the same way as the classical $q$-binomial coefficients refine the ordinary binomial coefficients.
Hou Sharon J. X.
Zeng Jiang
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