Congruences modulo powers of 2 for Fu's 5 dots bracelet partitions

Authors

  • E. X. W. Xia Jiangsu University
  • O. X. M. Yao Jiangsu University

Keywords:

congruences, 2-dissections, partitions, $k$ dots bracelet partitions

Abstract

In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamond partitions. Recently, Shishuo Fu generalised the notion of broken k-diamond partitions to combinatorial objects which he termed k dots bracelet partitions. Fu denoted the number of k dots bracelet partitions of n by Bk(n) and proved several congruences modulo primes and modulo powers of 2. More recently, Radu and Sellers extended the set of congruences proven by Fu by proving three congruences modulo squares of primes for B5(n), B7(n) and B11(n). In this note, we prove some congruences modulo powers of 2 for B5(n). For example, we find that for all integers n≥0, B5(16n+7)≡0(mod25). DOI: 10.1017/S0004972713000737

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles
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