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 permutations

Authors: Sophie Burrill 1; Marni Mishna 1; Jacob Post 2

  • 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 $k$.

https://doi.org/10.46298/dmtcs.2873
Source: HAL:hal-01186302v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: crossing,nesting,permutation,enumeration,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 1808.03764
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.disc.2020.111950
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1808.03764
  • 10.1016/j.disc.2020.111950
  • 10.1016/j.disc.2020.111950
  • 1808.03764
  • 10.48550/arxiv.1808.03764
Restricted permutations refined by number of crossings and nestings

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