论文标题
$（s，s+d，\ dots，s+pd）$ - 核心分区和理性的motzkin路径
The $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths
论文作者
论文摘要
在本文中，我们提出了$（s+d，d）$ - abacus $（s，s+d，\ dots，s+pd）$ - 核心分区，并在$（s，s+d，s+d，\ dots，s+pd，s+pd）$ - 核心分区和类型$（S型$（S+d d，d，-d）$（s+d，s+dots，s+dots，s+dots，s+dots，s+dots）之间。该结果不仅给出了$（s，s+d，\ dots，s+pd）$ - 核心分区的晶格路径解释，而且还用封闭的公式对其进行计数。另外，我们枚举$（s，s+1，\ dots，s+p）$ - 带有$ k $ corners和self-conconjugate $（s，s+1，\ dots，s+p）$ - 核心分区的核心分区。
In this paper, we propose an $(s+d,d)$-abacus for $(s,s+d,\dots,s+pd)$-core partitions and establish a bijection between the $(s,s+d,\dots,s+pd)$-core partitions and the rational Motzkin paths of type $(s+d,-d)$. This result not only gives a lattice path interpretation of the $(s,s+d,\dots,s+pd)$-core partitions but also counts them with a closed formula. Also we enumerate $(s,s+1,\dots,s+p)$-core partitions with $k$ corners and self-conjugate $(s,s+1,\dots,s+p)$-core partitions.
