## Factors of some lacunary $$q$$-binomial sums.(English)Zbl 1371.11044

Summary: In this paper, we prove a divisibility result for the lacunary $$q$$-binomial sum $\sum_{k \equiv r \quad (\text{mod } c)}(-1)^k q^{\binom{k}{2}}\left[\begin{matrix} n \\ k \end{matrix}\right]_q\left[\begin{matrix} (k-r)/c \\ l\end{matrix}\right]_{q^c}.$

### MSC:

 11B65 Binomial coefficients; factorials; $$q$$-identities 05A30 $$q$$-calculus and related topics 05A10 Factorials, binomial coefficients, combinatorial functions
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### References:

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