Strathprints logo
Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

The Möbius function of the permutation pattern Poset

Steingrimsson, Einar (2010) The Möbius function of the permutation pattern Poset. Journal of Combinatorics. 39–52.

[img]
Preview
PDF - Draft Version
Download (144Kb) | Preview

    Abstract

    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, in which case the Mobius function is shown to be either -1, 0 or 1. We conjecture that for intervals [\sigma,\tau] consisting of permutations avoiding the pattern 132, the magnitude of the Mobius function is bounded by the number of occurrences of \sigma in \tau. We also conjecture that the Mobius function of the interval [1,\tau] is -1, 0 or 1.

    Item type: Article
    ID code: 33800
    Keywords: permutation pattern poset, Möbius Function, Electronic computers. Computer science
    Subjects: Science > Mathematics > Electronic computers. Computer science
    Department: Faculty of Science > Computer and Information Sciences
    Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 19 Oct 2011 12:22
    Last modified: 04 Oct 2012 18:49
    URI: http://strathprints.strath.ac.uk/id/eprint/33800

    Actions (login required)

    View Item

    Fulltext Downloads: