论文标题
关于麦克马洪和Subbarao定理的概括
On generalizations of theorems of MacMahon and Subbarao
论文作者
论文摘要
在本文中，我们考虑了P.A.的各种定理。 Macmahon和M.V. Subbarao。对于非负整数$ n $，MacMahon证明了$ n $的分区数量，其中零件的多重性大于1，等于$ n $的分区数量，其中奇数零件与3 Modulo 6相一致。我们为此定理提供了新的证明，并为此提供了一个新的证明，并提供了一个新的证明，并提供了一个新的。我们还概括了Subbarao对安德鲁斯扩展的有限。这种概括是基于Glaisher对Euler映射的奇数分区的扩展，结果，卖方和FU给出的两者也得到了扩展。与卖方和FU固定两个残留类别的卖方和FU不同，我们的人考虑了所有可能的残留类别。此外，得出相关分区功能的某些算术特性
In this paper, we consider various theorems of P.A. MacMahon and M.V. Subbarao. For a non-negative integer $n$, MacMahon proved that the number of partitions of $n$ wherein parts have multiplicity greater than 1 is equal to the number of partitions of $n$ in which odd parts are congruent to 3 modulo 6. We give a new bijective proof for this theorem and its generalization, which consequently provides a new proof of Andrews' extension of the theorem. We also generalize Subbarao's finitization of Andrews' extension. This generalization is based on Glaisher's extension of Euler's mapping for odd-distinct partitions and as a result, a bijection given by Sellers and Fu is also extended. Unlike in the case of Sellers and Fu where two residue classes are fixed, ours takes into consideration all possible residue classes. Furthermore, some arithmetic properties of related partition functions are derived
