Infinite Families of Strange Partition Congruences for Broken 2-diamonds
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چکیده
In 2007 George E. Andrews and Peter Paule [1] introduced a new class of combinatorial objects called broken k-diamonds. Their generating functions connect to modular forms and give rise to a variety of partition congruences. In 2008 Song Heng Chan proved the first infinite family of congruences when k = 2. In this note we present two non-standard infinite families of broken 2-diamond congruences derived from work of Oliver Atkin and Morris Newman. In addition, four conjectures related to k = 3 and k = 5 are stated.
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تاریخ انتشار 2009