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  1. Home > Articles & Issues >
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  3. Avoiding maximal par ...
Article

Avoiding maximal parabolic subgroups of S_k

Toufik Mansour ORCID (1) (2), Alek Vainshtein (1) (2)
(1) Department of Computer Science [Haifa]
(2) Department of Mathematics [Haïfa]
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Imported on
March 26, 2015
Published on
January 1, 2000
Last modified on
March 31, 2025
Volume 4
vol. 4:1
DOI
10.46298/dmtcs.276
License
https://about.hal.science/hal-authorisation-v1
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Avoiding maximal parabolic subgroups of S_k

Toufik Mansour ORCID (1) (2), Alek Vainshtein (1) (2)
(1) Department of Computer Science [Haifa]
(2) Department of Mathematics [Haïfa]
Abstract
We find an explicit expression for the generating function of the number of permutations in S_n avoiding a subgroup of S_k generated by all but one simple transpositions. The generating function turns out to be rational, and its denominator is a rook polynomial for a rectangular board.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • permutations
  • forbidden patterns
  • parabolic subgroups
  • Laguerre polynomials
  • rook polynomials
Cited by

Source: OpenCitations

  • 132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

    Discrete Applied Mathematics

    Authors : Eric S. Egge, Toufik Mansour ORCID

    Journal reference : Volume 143, 2004, pp. 72-83

    DOI : 10.1016/j.dam.2003.12.007
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