5 核和 7 核分区的新无限同余族

Pub Date : 2024-04-10 DOI:10.1007/s10474-024-01424-z

Z. Meng, O. X. M. Yao

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引用次数: 0

摘要

最近，Fathima 和 Pore [4] 为 \(a_5(n)\) 建立了 modulo 3 的无穷同余族，为 \(a_7(n)\) 建立了 modulo 2 的同余族。受他们工作的启发，我们利用纽曼同素异形证明了一些新的无穷同素异形族，即 \(a_5(n)\) 的模 3 同素异形族和\(a_7(n)\) 的模 2 同素异形族。

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New infinite families of congruences for 5-core and 7-core partitions

Let \(a_t(n)\) denote the number of t-core partitions of n. In recent years, a number of congruences for \(a_t(n)\) have been discovered for some small t. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\). Motivated by their work, we prove some new infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\) by utilizing Newman's identities.

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