On recent congruence results of Andrews and Paule for broken k-diamonds
On recent congruence results of Andrews and Paule for broken k-diamonds
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DOI：
10.1017/s0004972700039010
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发表时间：
2007-02
影响因子：
0.7
通讯作者：
M. Hirschhorn;James A. Sellers
中科院分区：
文献类型：
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作者：
M. Hirschhorn;James A. Sellers
在他们最近的作品之一，乔治安德鲁斯和彼得保罗继续他们的研究分区功能通过麦克马洪的分区分析考虑分区功能与有向图，其中包括链的六边形。在这个过程中，他们证明了一个与这些配分函数之一相关的同余，并推测了一些类似的同余结果。我们的第一个目标是在本说明中重新证明这个一致性，明确找到生成函数的问题。然后，我们证明了一个由安德鲁斯和保勒以及一些同余式没有提到他们所构成的。我们所有的结果都遵循简单的生成函数操作。
In one of their most recent works, George Andrews and Peter Paule continue their study of partition functions via MacMahon's Partition Analysis by considering partition functions associated with directed graphs which consist of chains of hexagons. In the process, they prove a congruence related to one of these partition functions and conjecture a number of similar congruence results. Our first goal in this note is to reprove this congruence by explicitly finding the generating function in question. We then prove one of the conjectures posed by Andrews and Paule as well as a number of congruences not mentioned by them. All of our results follow from straightforward generating function manipulations.