Factors of the Gaussian coefficients

Abstract. We present some simple observations on factors of the qbinomial coefficients, the q-Catalan numbers, and the q-multinomial coefficients. Writing the Gaussian coefficient with numerator n and denominator k in a form such that 2k n by the symmetry in k, we show that this coefficient has at least k factors. Some divisibility results of Andrews, Brunetti and Del Lungo are also discussed.

• Type: Journal
• Year: 2006
• Where: DM
• Authors: William Y. C. Chen, Qing-Hu Hou
• Keywords: DM 2006, Gaussian Coefficient, Q-multinomial Coefficients, Qbinomial Coefficients