Sophie Burrill ; Marni Mishna ; Jacob Post
-
On $k$-crossings and $k$-nestings of permutations
dmtcs:2873 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
-
https://doi.org/10.46298/dmtcs.2873
On $k$-crossings and $k$-nestings of permutationsArticle
Authors: Sophie Burrill 1; Marni Mishna 1; Jacob Post 2
NULL##NULL##NULL
Sophie Burrill;Marni Mishna;Jacob Post
1 Department of Mathematics [Burnaby]
2 Department of Computer Science
We introduce $k$-crossings and $k$-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number of $k$-noncrossing permutations is equal to the number of $k$-nonnesting permutations. We also provide some enumerative results for $k$-noncrossing permutations for some values of $k$.
Sophie Burrill;Sergi Elizalde;Marni Mishna;Lily Yen, 2016, A Generating Tree Approach to k-Nonnesting Partitions and Permutations, arXiv (Cornell University), 20, 3, pp. 453-485, 10.1007/s00026-016-0321-1, https://arxiv.org/abs/1108.5615.
Adel Hamdi, 2011, Symmetric Distribution of Crossings and Nestings in Permutations of Type $B$, The Electronic Journal of Combinatorics, 18, 1, 10.37236/687, https://doi.org/10.37236/687.