Congruences modulo 11 for broken 5-diamond partitions

Eric H. Liu, James A. Sellers, Ernest X.W. Xia

Research output: Contribution to journalArticle

Abstract

The notion of broken k-diamond partitions was introduced by Andrews and Paule in 2007. For a fixed positive integer k, let Δ k(n) denote the number of broken k-diamond partitions of n. Recently, Paule and Radu conjectured two relations on Δ 5(n) which were proved by Xiong and Jameson, respectively. In this paper, employing these relations, we prove that, for any prime p with p≡1(mod4), there exists an integer λ(p)∈{2,3,5,6,11} such that, for n, α≥ 0 , if p∤ (2 n+ 1) , then (Folmula presented.).Moreover, some non-standard congruences modulo 11 for Δ 5(n) are deduced. For example, we prove that, for α≥ 0 , Δ5(11×55α+12)≡7(mod11).

Original languageEnglish (US)
Pages (from-to)151-159
Number of pages9
JournalRamanujan Journal
Volume46
Issue number1
DOIs
StatePublished - May 1 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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