拉马努金的θ函数与分拆的分部奇偶性及曲柄
Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions.
作者信息
Banerjee Koustav, Dastidar Manosij Ghosh
机构信息
Research Institute for Symbolic Computation, Johannes Kepler University, Altenberger Strasse 69, 4040 Linz, Austria.
Technische Universität Wien, Wiedner Hauptstrasse 8-10/104, 1040 Wien, Austria.
出版信息
Ann Comb. 2023;27(3):565-578. doi: 10.1007/s00026-022-00615-1. Epub 2022 Oct 25.
In this paper, we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation with the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.
在本文中，我们探讨拉马努金θ函数与一类根据其部分的奇偶性定义的分拆函数之间的复杂联系。这进而引导我们对分拆的曲柄进行奇偶性分析，以及它与具有奇数个部分的分拆数、自共轭分拆，还有与杜尔费正方形和弗罗贝尼乌斯符号的相关性。
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