Journal of Combinatorics

Volume 6 (2015)

Number 1–2

Signed arc permutations

Pages: 205 – 234

DOI: https://dx.doi.org/10.4310/JOC.2015.v6.n1.a11

Authors

Sergi Elizalde (Department of Mathematics, Dartmouth College, Hanover, New Hampshire, U.S.A.)

Yuval Roichman (Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel)

Abstract

Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed enumeration formulas with respect to their descent set and major index. Next, we generalize the notion of arc permutations to the hyperoctahedral group in two different directions. We show that these extensions to type $B$ carry interesting analogues of the properties of type $A$ arc permutations, such as characterizations by pattern avoidance, and elegant unsigned and signed enumeration formulas with respect to the flag-major index.

Keywords

arc permutation, pattern avoidance, descent set, hyperoctahedral group, signed enumerator, flag-major index

2010 Mathematics Subject Classification

Primary 05A05, 05E18. Secondary 05A15, 05A19, 05E10.

Published 20 March 2015