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arXiv · 2207.06712

On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8

James A. Sellers·Nicolas Allen Smoot
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Abstract

In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the $k$-elongated plane partition function $d_k(n)$ by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function $d_7(n)$. We prove that such a congruence family exists -- indeed, for powers of 8. The proof utilizes only classical methods, i.e., integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for $d_k(n)$ which require more modern methods to prove.

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BibTeXRIS

James A. Sellers, Nicolas Allen Smoot. 2022-07-14. On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8. https://arxiv.org/abs/2207.06712

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