Infinite families of strange partition congruences for broken 2-diamonds
Infinite families of strange partition congruences for broken 2-diamonds
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DOI：
10.1007/s11139-010-9283-9
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
P. Paule;S. Radu
中科院分区：
文献类型：
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作者：
P. Paule;S. Radu
2007年，乔治·E·安德鲁斯和彼得·保勒(Acta Arithmetica 126：281-294,2007)引入了一类新的组合物体，称为断钻。它们的母函数与模形式相联系，并产生各种划分同余。2008年，宋恒证明了k=2时的第一个无限族同余。在这篇注记中，我们给出了Oliver Atkin和Morris Newman工作的两个非标准的破碎2-钻石同余的无限族。此外，还提出了与k=3和k=5有关的四个猜想。
In 2007, George E. Andrews and Peter Paule (Acta Arithmetica 126:281–294, 2007) introduced a new class of combinatorial objects called brokenk-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 whenk=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 tok=3 andk=5 are stated.