论文标题
钢筋分区，核心移动的年轻图和两倍不同的核心的结果
Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores
论文作者
论文摘要
自从Morris和Yaseen引入了酒吧核的概念以来，已经研究了同时研究的核心核，核心移动的年轻图（或CSYDS）以及两倍不同的核心。在本文中，我们的目标是为$（s，t）$ - 核心和$（S，S+D，S+2D）$ - 核心的这些核心分区的数量提供一个公式，以介绍其余尚未涵盖的情况。为了实现这一目标，我们观察到$ \ bar {s} $ - 核心分区的特征，以获得双倍的$ s $ core分区和$ s $ cys的特征。通过使用它们，我们在$（s，t）$ - 核心上构建了这些核心分区的$ NE $ lattice路径解释。此外，我们在$（S，S+D，S+2D）$ - 内核上对这些核心分区的免费Motzkin路径解释。
Simultaneous bar-cores, core shifted Young diagrams (or CSYDs), and doubled distinct cores have been studied since Morris and Yaseen introduced the concept of bar-cores. In this paper, our goal is to give a formula for the number of these core partitions on $(s,t)$-cores and $(s,s+d,s+2d)$-cores for the remaining cases that are not covered yet. In order to achieve this goal, we observe a characterization of $\bar{s}$-core partitions to obtain characterizations of doubled distinct $s$-core partitions and $s$-CSYDs. By using them, we construct $NE$ lattice path interpretations of these core partitions on $(s,t)$-cores. Also, we give free Motzkin path interpretations of these core partitions on $(s,s+d,s+2d)$-cores.
