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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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