# 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). B68a. ISSN 1286-4889

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## 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.

#### ORCID iDs

Kitaev, Sergey ORCID: https://orcid.org/0000-0003-3324-1647 and Remmel, Jeffrey;
• Item type: Article 49896 DateEventMarch 2012Published permutation statistics, marked mesh patterns, distribution, alternating permutations, Mathematics Science > Mathematics Faculty of Science > Computer and Information Sciences Pure Administrator 17 Oct 2014 15:23 18 Jan 2023 09:48 https://strathprints.strath.ac.uk/id/eprint/49896