Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415555 | Journal of Number Theory | 2013 | 14 Pages |
Abstract
In 2007, Andrews and Paule introduced the family of functions Îk(n) which enumerate the number of broken k-diamond partitions for a fixed positive integer k. Since then, numerous mathematicians have considered partitions congruences satisfied by Îk(n) for small values of k. In this work, we provide an extensive analysis of the parity of the function Î3(n), including a number of Ramanujan-like congruences modulo 2. This will be accomplished by completely characterizing the values of Î3(8n+r) modulo 2 for râ{1,2,3,4,5,7} and any value of n⩾0. In contrast, we conjecture that, for any integers 0⩽B
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Silviu Radu, James A. Sellers,