6 research outputs found
Generating trees and pattern avoidance in alternating permutations
We extend earlier work of the same author to enumerate alternating
permutations avoiding the permutation pattern 2143. We use a generating tree
approach to construct a recursive bijection between the set A_{2n}(2143) of
alternating permutations of length 2n avoiding 2143 and standard Young tableaux
of shape (n, n, n) and between the set A_{2n + 1}(2143) of alternating
permutations of length 2n + 1 avoiding 2143 and shifted standard Young tableaux
of shape (n + 2, n + 1, n). We also give a number of conjectures and open
questions on pattern avoidance in alternating permutations and generalizations
thereof.Comment: 21 pages. To be presented at FPSAC 2010. Comments welcome
Pattern avoidance for alternating permutations and reading words of tableaux
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 67-69).We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of permutations that are the reading words of a "thickened staircase" shape (or equivalently of permutations with descent set {k, 2k, 3k, . . .}) avoiding a monotone pattern, and of the reading words of Young tableaux of any skew shape avoiding any of the patterns 132, 213, 312, or 231. Our bijections include a simple bijection involving binary trees, variations on the Robinson-Schensted-Knuth correspondence, and recursive bijections established via isomorphisms of generating trees.by Joel Brewster Lewis.Ph.D