A Survey of Alternating Permutations
Name
Stanley_A survey.pdf
Size
380.06 KB
Format
Adobe PDF
Checksum (MD5)
62bffb4c4e34e5523c12b868812c9251
Author(s)
Stanley, Richard P.
Date Issued
January 2010
Journal
Combinatorics and Graphs
Publisher
American Mathematical Society
Citation
Stanley, Richard P. "A Survey of Alternating Permutations." in Combinatorics and Graphs: the twentieth anniversary conference of IPM Combinatorics, May 15-21, 2009, Tehran, Iran, edited by Richard A. Brualdi, Samad Hedayat, Hadi Kharaghani, Gholamriza B. Khosrovshahi and Shahrair Shahrairi.(in Contemporary Mathematics), American Mathematical Society, 2010.
Version
Author's final manuscript
Abstract
A permutation a1a2 · · · an of 1, 2, . . . , n is alternating if a1 > a2 <
a3 > a4 < · · · . We survey some aspects of the theory of alternating permutations,
beginning with the famous result of Andr´e that if En is the number
of alternating permutations of 1, 2, . . . , n, then ... = sec x + tan x.
Topics include refinements and q-analogues of En, various occurrences of En in
mathematics, longest alternating subsequences of permutations, umbral enumeration
of special classes of alternating permutations, and the connection
between alternating permutations and the cd-index of the symmetric group.
Description
Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
http://www.ams.org/bookstore-getitem/item=conm-531
