The Möbius function of the permutation pattern Poset
Steingrimsson, Einar (2010) The Möbius function of the permutation pattern Poset. Journal of Combinatorics. 39–52. (http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.4011...)
Preview 
PDF.
Filename: 0902.4011v3.pdf
Preprint 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 Dates: DateEvent2010PublishedSubjects: 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: 08 Aug 2024 01:05 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/33800