Bernini, A. and Ferrari, L. and Steingrimsson, E. (2011) The Möbius function of the consecutive pattern poset. The Electronic Journal of Combinatorics, 18 (1).

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Abstract
An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset. For most intervals our results give an immediate answer to the question. In the remaining cases, we give a polynomial time algorithm to compute the Möbius function. In particular, we show that the Möbius function only takes the values −1, 0 and 1.
Item type:  Article 

ID code:  33801 
Keywords:  consecutive pattern poset , Möbius function , Electronic computers. Computer science, Computational Theory and Mathematics, Geometry and Topology, Theoretical 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 11:15 
Last modified:  26 Mar 2015 16:00 
URI:  http://strathprints.strath.ac.uk/id/eprint/33801 
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