| Autor: |
Bonichon, Nicolas, Morel, Pierre-Jean |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Journal of Integer Sequences, Vol. 25: Article 22.8.3, 2022 |
| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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