Picture of a sphere with binary code

Making Strathclyde research discoverable to the world...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. It exposes Strathclyde's world leading Open Access research to many of the world's leading resource discovery tools, and from there onto the screens of researchers around the world.

Explore Strathclyde Open Access research content

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 - Draft Version

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.