Elementary proofs of infinitely many congruences for \(k\)-elongated partition diamonds (Q2166280)

Several congruence properties satisfied by \(d_k(n)\), the number of \(k\)-elongated plane partition diamonds of length \(n\), was recently established for \(k\in\{1,2,3\}\) by \textit{G. E. Andrews} and \textit{P. Paule} [J. Number Theory 234, 95--119 (2022; Zbl 1484.11201)] using modular forms as their primary proof tool. In this paper, the authors extend some of the results proven by Andrews and Paule by proving infinitely many congruence properties satisfied by the functions \(d_k\) for an infinite set of values of \(k\). The proof techniques employed are all elementary, relying on generating function manipulations and classical \(q\)-series results.