标题： 高维布局图与Baxter d-排列 显示英文标题

标题： Higher dimensional floorplans and Baxter d-permutations

摘要： 一个 $2-$维马赛克地板平面图是一个矩形通过其他矩形分割而成，且没有空房间。 这些分割（考虑某些变形后）已知与 Baxter 排列一一对应。 $d$-地板平面图是马赛克地板平面图在更高维度的推广，而 $d$-排列是一个 $(d-1)$-置换元组。 最近，N. 邦尼雄和P.-J. 莫雷尔在文章 {\it 整数序列杂志} 25 (2022) 中引入了广义的 Baxter $d$-排列，该排列推广了通常的 Baxter 排列。 本文中，我们研究任意维度的镶嵌平面图，并构建了用于生成$d$-平面图的生成树，该生成树推广了已知的用于生成$2$-平面图的生成树结构。 对应的标记和重写规则在更高维度下似乎明显更加复杂。 此外，我们给出了$2^{d-1}$-平面图与由禁止链接模式表征的$d$-排列之间的双射关系。 令人惊讶的是，这组$d$-排列严格包含于 Baxter$d$-排列之中。 显示英文摘要

摘要： A $2-$dimensional mosaic floorplan is a partition of a rectangle by other rectangles with no empty rooms. These partitions (considered up to some deformations) are known to be in bijection with Baxter permutations. A $d$-floorplan is the generalisation of mosaic floorplans in higher dimensions, and a $d$-permutation is a $(d-1)$-tuple of permutations. Recently, in N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), Baxter $d$-permutations generalising the usual Baxter permutations were introduced. In this paper, we consider mosaic floorplans in arbitrary dimensions, and we construct a generating tree for $d$-floorplans, which generalises the known generating tree structure for $2$-floorplans. The corresponding labels and rewriting rules appear to be significantly more involved in higher dimensions. Moreover we give a bijection between the $2^{d-1}$-floorplans and $d$-permutations characterized by forbidden vincular patterns. Surprisingly, this set of $d$-permutations is strictly contained within the set of Baxter $d$-permutations.