Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks
Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks
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DOI：
10.1007/s00222-007-0043-4
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发表时间：
2007-03
影响因子：
3.1
通讯作者：
G. Andrews
中科院分区：
文献类型：
--
作者：
G. Andrews
阿特金和加文介绍了时刻的行列分区在他们的工作连接行列和曲柄。在这里，我们考虑这些时刻的组合解释。这需要引入一种新的分区表示法，即Durfee符号，以及随后的改进。这反过来又导致我们的各种新的一致性，为我们的'标记'杜尔菲符号很大程度上的精神戴森的原始插图的行列分区。
Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cranks. Here we consider a combinatorial interpretation of these moments. This requires the introduction of a new representation for partitions, the Durfee symbol, and subsequent refinements. This in turn leads us to a variety of new congruences for our ‘marked’ Durfee symbols much in the spirit of Dyson’s original conjectures on the ranks of partitions.