English

Congruences modulo powers of $7$ for $k$-elongated plane partitions

Number Theory 2025-08-19 v2 Combinatorics

Abstract

The enumeration dk(n)d_k(n) of kk-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function p(n)p(n). Congruences for dk(n)d_k(n) modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for d5(n)d_5(n) modulo powers of 5. In this paper we have discovered an infinite congruence family for d3(n)d_3(n) and d5(n)d_5(n) modulo powers of 7.

Keywords

Cite

@article{arxiv.2508.09723,
  title  = {Congruences modulo powers of $7$ for $k$-elongated plane partitions},
  author = {Dandan Chen and Tianjian Xu and Siyu Yin},
  journal= {arXiv preprint arXiv:2508.09723},
  year   = {2025}
}

Comments

23 pages