By Shane Chern

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

March 26, 2020

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

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