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arXiv · 0907.2870

On the least common multiple of $q$-binomial coefficients

Victor J. W. Guo
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Abstract

In this paper, we prove the following identity $$ \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].

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Victor J. W. Guo. 2009-07-16. On the least common multiple of $q$-binomial coefficients. https://doi.org/10.1515/integ.2010.029

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