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1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5

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Abstract

Let s(n) be the number of 1-shell totally symmetric plane partitions (TSPPs) of n. In this paper, an infinite family of congruences modulo powers of 5 for s(n) will be deduced through an elementary approach. Namely,

$$\begin{aligned} s\left( 2\cdot 5^{2\alpha -1}n+5^{2\alpha -1}\right) \equiv 0 \pmod {5^{\alpha }}. \end{aligned}$$

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Acknowledgements

I would like to acknowledge my gratitude to the referee for helpful comments on an earlier draft of this paper.

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  1. Department of Mathematics, Penn State University, University Park, State College, PA, 16802, USA

    Shane Chern

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  1. Shane Chern
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Correspondence to Shane Chern.

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Chern, S. 1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5. Ramanujan J 55, 713–731 (2021). https://doi.org/10.1007/s11139-020-00306-6

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