论文标题
关于贝克的分区统计数据的陈莫·osburn的某些猜想的证明
Proofs of some conjectures of Chan-Mao-Osburn on Beck's partition statistics
论文作者
论文摘要
最近，乔治·贝克（George Beck）介绍了两个分区统计$ nt（m，j，n）$和$m_Ω（m，j，n）$，它表示$ n $的分区中的零件总数，以及与$ m $ modulo $ j $一致的等级，以及与$ n $ $ $ moduloent的分配中的零件总数。安德鲁斯（Andrews）证明了由贝克（Beck）猜想的$ NT（M，5，N）$的一致性。最近，Chan，Mao和Osburn建立了许多Andrews-Beck类型的一致性，并提出了一些涉及$ NT（M，J，N）$和$M_Ω（M，J，N）$的猜想。其中一些猜想是由Chern和Mao证明的。在本文中，我们确认了陈-Mao-osburn的其余三个猜想，以及由于毛泽东而引起的两个猜想。我们还提出了$m_Ω（m，j，n）$和$ nt（m，j，n）$的两个新猜想。
Recently, George Beck introduced two partition statistics $NT(m,j,n)$ and $M_ω(m,j,n)$, which denote the total number of parts in the partition of $n$ with rank congruent to $m$ modulo $j$ and the total number of ones in the partition of $n$ with crank congruent to $m$ modulo $j$, respectively. Andrews proved a congruence on $NT(m,5,n)$ which was conjectured by Beck. Very recently, Chan, Mao and Osburn established a number of Andrews-Beck type congruences and posed several conjectures involving $NT(m,j,n)$ and $M_ω(m,j,n)$. Some of those conjectures were proved by Chern and Mao. In this paper, we confirm the remainder three conjectures of Chan-Mao-Osburn and two conjectures due to Mao. We also present two new conjectures on $M_ω(m,j,n)$ and $NT(m,j,n)$.
