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

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 ${\left[\genfrac{}{}{0ex}{}{n}{k}\right]}_q$ 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)].

5 pages

References in corpus (1)

• Some Arithmetic Properties of the q-Euler Numbers and q-Salié Numbers