论文标题
对称的Dyck瓷砖，投票表和树状的tableaux的形状
Symmetric Dyck tilings, ballot tableaux and tree-like tableaux of shifted shapes
论文作者
论文摘要
对称的Dyck瓷砖和投票瓷砖是该地区的某些瓷砖，周围是两个投票路径。我们研究了与对称的堤防瓷砖（如树木，赫米特历史和完美匹配）的对称性堤防瓷砖的组合物体的关系。我们还在标记的树上介绍了两种操作，用于对称型戴克瓷砖：对称的戴克瓷砖带（SYMDTS）和对称的Dyck瓷砖丝带（Symdtr）。我们给出了两个针对对称戴克瓷砖的Hermite历史的定义，并表明它们通过使用Symdts操作与Hermite历史之间的对应关系相同。由于投票瓷砖在对称型戴克瓷砖的集合中形成了一个子集，因此我们从标记的树木中构造了一个包容性的地图，用于投票瓷砖，以标记为对称型戴克瓷砖的树木。通过此包容性地图，可以将对称型戴克瓷砖的结果应用于投票砖的结果。我们介绍并研究了投票表格和类似树状形状的树状的概念，这些概念分别是Dyck Tableaux和类似树状的Tableaux的概括。通过使用Symdtr操作和标记的树的结构，用于对称型型型甲米之间，给出了投票tableaux和类似树状形状的树状tableaux之间的对应关系。
Symmetric Dyck tilings and ballot tilings are certain tilings in the region surrounded by two ballot paths. We study the relations of combinatorial objects which are bijective to symmetric Dyck tilings such as labeled trees, Hermite histories, and perfect matchings. We also introduce two operations on labeled trees for symmetric Dyck tilings: symmetric Dyck tiling strip (symDTS) and symmetric Dyck tiling ribbon (symDTR). We give two definitions of Hermite histories for symmetric Dyck tilings, and show that they are equivalent by use of the correspondence between symDTS operation and an Hermite history. Since ballot tilings form a subset in the set of symmetric Dyck tilings, we construct an inclusive map from labeled trees for ballot tilings to labeled trees for symmetric Dyck tilings. By this inclusive map, the results for symmetric Dyck tilings can be applied to those of ballot tilings. We introduce and study the notions of ballot tableaux and tree-like tableaux of shifted shapes, which are generalizations of Dyck tableaux and tree-like tableaux, respectively. The correspondence between ballot tableaux and tree-like tableaux of shifted shapes is given by using the symDTR operation and the structure of labeled trees for symmetric Dyck tilings.
