Factors of the Gaussian coefficients |
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Authors: | William YC Chen |
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Institution: | Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China |
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Abstract: | We present some simple observations on factors of the q-binomial 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. |
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Keywords: | q-Multinomial coefficient Gaussian coefficient q-Catalan number Cyclotomic polynomial |
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