论文标题
在$ d $ - permutations and todate避免课程
On $d$-permutations and Pattern Avoidance Classes
论文作者
论文摘要
多维排列或$ d $ permutations在$ [n]^d $上的图表表示，使得满足$ x_i = j $ for in [d] $ in [d] $和$ j \ in [n] $中的$ x_i = j $ for $ x_i = j $的每个点有一个点。 Bonichon和Morel先前列举了$ 3 $ permutations避免了小图案，我们首先证明了四个猜想，详尽地列举了$ 3 $ - permutations，避免了$ 3 $的任何两种固定模式。我们进一步提供了一个枚举结果，该结果将$ 3 $ permuont的避免班级与各自的复发关系有关。特别是，我们以$ 3 $ permutations避免了$ 132 $和$ 213 $的复发关系，这为OEIS数据库贡献了新的序列。然后，我们将结果扩展到完全枚举$ 3 $ permutations，避免了三种大小$ 3 $的模式。
Multidimensional permutations, or $d$-permutations, are represented by their diagrams on $[n]^d$ such that there exists exactly one point per hyperplane $x_i$ that satisfies $x_i= j$ for $i \in [d]$ and $j \in [n]$. Bonichon and Morel previously enumerated $3$-permutations avoiding small patterns, and we extend their results by first proving four conjectures, which exhaustively enumerate $3$-permutations avoiding any two fixed patterns of size $3$. We further provide a enumerative result relating $3$-permutation avoidance classes with their respective recurrence relations. In particular, we show a recurrence relation for $3$-permutations avoiding the patterns $132$ and $213$, which contributes a new sequence to the OEIS database. We then extend our results to completely enumerate $3$-permutations avoiding three patterns of size $3$.
