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

Shane Chern

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

Number Theory 2020-03-30 v2 Combinatorics

Authors: Shane Chern

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

Keywords

totally symmetric plane partitions congruences powers of 5 elementary approach

Cite

@article{arxiv.1802.04344,
  title  = {1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5},
  author = {Shane Chern},
  journal= {arXiv preprint arXiv:1802.04344},
  year   = {2020}
}

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