The Möbius function of the consecutive pattern poset

Tools

Bernini, A. and Ferrari, L. and Steingrimsson, E. (2011) The Möbius function of the consecutive pattern poset. The Electronic Journal of Combinatorics, 18 (1). P146.

[thumbnail of 1103.0173v1.pdf]
Preview
 PDF. Filename: 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.

ORCID iDs

Bernini, A., Ferrari, L. and Steingrimsson, E. ORCID logoORCID: https://orcid.org/0000-0003-4611-0849;
CORE (COnnecting REpositories)