The Möbius function of the permutation pattern Poset

@article{Steingrmsson2009TheMF,
  title={The M{\"o}bius function of the permutation pattern Poset},
  author={E. Steingr{\'i}msson and Bridget Eileen Tenner},
  journal={The Journal of Combinatorics},
  year={2009},
  volume={1},
  pages={39-52}
}
  • E. Steingrímsson, Bridget Eileen Tenner
  • Published 2009
  • Mathematics
  • The Journal of Combinatorics
  • A permutation \tau contains another permutation \sigma as a pattern if \tau has a subsequence whose elements are in the same order with respect to size as the elements in \sigma. This defines a partial order on the set of all permutations, and gives a graded poset P. We give a large class of pairs of permutations whose intervals in P have Mobius function 0. Also, we give a solution to the problem when \sigma occurs precisely once in \tau, and \sigma and \tau satisfy certain further conditions… CONTINUE READING
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    References

    SHOWING 1-8 OF 8 REFERENCES
    The patterns of permutations
    • H. Wilf
    • Computer Science, Mathematics
    • Discret. Math.
    • 2002
    • 75
    • PDF
    The Möbius function of a composition poset
    • 40
    • PDF
    The enumeration of simple permutations.
    • 79
    • PDF
    Enumerative combinatorics
    • 3,267
    Cambridge Studies in Advanced Mathematics
    • 668
    Iceland E-mail address: einarst@ru.is Department of Mathematical Sciences
    • Iceland E-mail address: einarst@ru.is Department of Mathematical Sciences
    The patterns of permutations, Discrete Math
    • The patterns of permutations, Discrete Math
    • 2002