caa a22 4500 463178025 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s11139-007-9051-7 doi (NATIONALLICENCE)springer-10.1007/s11139-007-9051-7 Two new families of q -positive integers [Elektronische Daten] [Sharon Hou, Jiang Zeng] Let n,p and k be three non negative integers. We prove that the apparently rational fractions of q: $$\begin{array}{l}{n\brack k}_{q}{}_{3}\phi_{2}\left[\matrix{q^{1-k},q^{-p},q^{p-n}\\q,q^{1-n}\\}\bigg|q;q^{k+1}\right]\quad \hbox{and}\quad \\[12pt]q^{(n-p)p}{n\brack k}_{q}{}_{3}\phi_{2}\left[\matrix{q^{1-k},q^{-p},q^{p-n}\\q,q^{1-n}\\}\bigg|q;q\right]\end{array}$$ are actually polynomials of q with non negative integer coefficients. This generalizes a recent result of Lassalle (Ann. Comb. 6(3-4), 399-405, 2002), in the same way as the classical q-binomial coefficients refine the ordinary binomial coefficients. Springer Science+Business Media, LLC, 2007 q -binomial coefficients nationallicence q -integers nationallicence Basic hypergeometric functions nationallicence Hou Sharon Center for Combinatorics, LPMC, Nankai University, 300071, Tianjin, People's Republic of China aut Zeng Jiang Institut Camille Jordan, Université Claude Bernard (Lyon I), 69622, Villeurbanne Cedex, France aut The Ramanujan Journal Springer US; http://www.springer-ny.com 14/3(2007-12-01), 421-435 1382-4090 14:3<421 2007 14 11139 https://doi.org/10.1007/s11139-007-9051-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-007-9051-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hou Sharon Center for Combinatorics, LPMC, Nankai University, 300071, Tianjin, People's Republic of China aut NATIONALLICENCE 700 1- Zeng Jiang Institut Camille Jordan, Université Claude Bernard (Lyon I), 69622, Villeurbanne Cedex, France aut NATIONALLICENCE 773 0- The Ramanujan Journal Springer US; http://www.springer-ny.com 14/3(2007-12-01), 421-435 1382-4090 14:3<421 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer