论文标题
baxter $ d $ - permutations和其他模式避免了课程
Baxter $d$-permutations and other pattern avoiding classes
论文作者
论文摘要
大小$ n $的排列可以识别为其图表，其中每行恰好有一个点和列中的一个点$ [n]^2 $。在本文中，我们考虑了多维排列（或$ d $ - permutations），这些排列在网格$ [n]^d $上被标识为它们的图表，其中每个超平面$ x_i = j $ for $ i \ in [d] $ in [d] $ in [d] $和$ j \ in [n] $中。我们首先详尽地研究所有小模式以避免课程。我们提供了一些射击，以列举其中的一些班级，并为其他阶级提出一些猜想。然后，我们将经过良好研究的Baxter排列概括为这一多维环境。此外，我们还提供了百特$ d $ permutations的尺寸图案避免表征。
A permutation of size $n$ can be identified to its diagram in which there is exactly one point per row and column in the grid $[n]^2$. In this paper we consider multidimensional permutations (or $d$-permutations), which are identified to their diagrams on the grid $[n]^d$ in which there is exactly one point per hyperplane $x_i=j$ for $i\in[d]$ and $j\in[n]$. We first investigate exhaustively all small pattern avoiding classes. We provide some bijection to enumerate some of these classes and we propose some conjectures for others. We then give a generalization of well-studied Baxter permutations into this multidimensional setting. In addition, we provide a vincular pattern avoidance characterization of Baxter $d$-permutations.
