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
0902.4011v3.pdf - Draft Version

Download (148kB) | 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
Depositing user: Pure Administrator
Date Deposited: 19 Oct 2011 11:22
Last modified: 27 Mar 2015 15:49
URI: http://strathprints.strath.ac.uk/id/eprint/33800

Actions (login required)

View Item View Item