A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions

2024/12/06 by Chen, Dandan, Chen, Rong, Yin, Siyu
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.04998

Abstract

In 2007, Andrews and Paule introduced the family of functions Δ_k(n), which enumerate the number of broken k-diamond partitions for a fixed positive integer k. In 2013, Radu and Sellers completely characterized the parity of Δ₃(8n + r) for some r and gave a conjecture on congruences modulo powers of 2 for broken 3-diamond partitions. We use an unconventional U-sequence to solve the revised conjecture proposed by Radu and Sellers.

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