Pattern avoidance for alternating permutations and reading words of tableaux
Name
809654848-MIT.pdf
Description
Full printable version
Size
572.16 KB
Format
Adobe PDF
Checksum (MD5)
c5314304ef061cf66673506f3f435937
Author(s)
Lewis, Joel Brewster
Advisor(s)
Alexander Postnikov.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
M.I.T. theses are protected by
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission.
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission.
Persistent DSpace Link
