Journal of Integer Sequences, Vol. 21 (2018), Article 18.5.8

New Congruences for Broken k-Diamond Partitions

Dazhao Tang
College of Mathematics and Statistics
Huxi Campus
Chongqing University
Chongqing—401 331
PR China


Andrews and Paule introduced a new class of directed graphs, called broken k-diamond partitions. Let Δk(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k. In this paper, we establish new infinite families of congruences modulo 5, 7, 25 and 49 for Δk(n) via a standard q-series technique and modular forms.

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Received September 11 2017; revised versions received June 26 2018; June 29 2018. Published in Journal of Integer Sequences, July 1 2018.

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