Picture map of Europe with pins indicating European capital cities

Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

Explore research outputs by the European Policies Research Centre...

Quadrant marked mesh patterns in alternating permutations

Kitaev, Sergey and Remmel, Jeffrey (2012) Quadrant marked mesh patterns in alternating permutations. Séminaire Lotharingien de Combinatoire (68). ISSN 1286-4889

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

This paper is a continuation of the systematic study of the distribution of quadrant marked mesh patterns initiated in [J. Integer Sequences, 12 (2012), Article 12.4.7]. We study quadrant marked mesh patterns on up-down and down-up permutations, also known as alternating and reverse alternating permutations, respectively. In particular, we refine classical enumeration results of André [C. R. Acad. Sci. Paris 88 (1879), 965-967; J. Math. Pur. Appl. 7 (1881), 167-184] on alternating permutations by showing that the distribution with respect to the quadrant marked mesh pattern of interest is given by (sec(xt))1/x on up-down permutations of even length and by $ \int_0^t (\sec(xz))^{1+\frac{1}{x}}dz$ on down-up permutations of odd length.