Quadrant marked mesh patterns in alternating permutations

Sergey Kitaev, Jeffrey Remmel

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article numberB68a
Number of pages20
JournalSéminaire Lotharingien de Combinatoire
Issue number68
Publication statusPublished - Mar 2012


  • permutation statistics
  • marked mesh patterns
  • distribution
  • alternating permutations


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