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On the divisibility of q-trinomial coefficients

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Abstract

We investigate the divisibility of the q-trinomial coefficients introduced by Andrews and Baxter, which is analogous to the q-Wolstenholme theorem regarding the q-binomial coefficients. A congruence for sums of central q-binomial coefficients is also established.

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Acknowledgements

The author would like to thank Ofir Gorodetsky for discussions on q-trinomial coefficients and useful suggestions regarding the paper. The author is also grateful to the anonymous referee for his/her helpful comments which helped to improve the exposition of the paper.

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  1. Department of Mathematics, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Ji-Cai Liu

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This work was supported by the National Natural Science Foundation of China (Grant 12171370)

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Liu, JC. On the divisibility of q-trinomial coefficients. Ramanujan J 60, 455–462 (2023). https://doi.org/10.1007/s11139-022-00558-4

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