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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 permutationsConference paper

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

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