Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

The Möbius function of the consecutive pattern poset

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

[img]
Preview
PDF
1103.0173v1.pdf - Preprint

Download (149kB) | Preview

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.