Parity results for broken 11-diamond partitions

Abstract

Abstract Recently, Dai proved new infinite families of congruences modulo 2 for broken 11-diamond partition functions by using Hecke operators. In this note, we establish new parity results for broken 11-diamond partition functions. In particular, we generalize the congruences due to Dai by utilizing an identity due to Newman. Furthermore, we prove some strange congruences modulo 2 for broken 11-diamond partition functions. For example, we prove that if p is a prime with p ≠ 23 and Δ11(2p + 1) ≡ 1 (mod 2), then for any k ≥ 0, Δ11(2p3k+3 + 1) ≡ 1 (mod 2), where Δ11(n) is the number of broken 11-diamond partitions of n.