A Survey of Alternating Permutations

By Richard P. Stanley. 2009

206 citations recorded by the source corpus.

A permutation a1a2 ···an of 1,2,...,n is alternating if a1 > a2 a4 < ···. We survey some aspects of the theory of alternating permu- tations, beginning with the famous result of Andre that if En is the number of alternating permutations of 1,2,...,n, then P n�0 En x n n! = secx + tanx. Topics include refinements and q-analogues of En, various occurrences of En in mathematics, longest alternating subsequences of permutations, umbral enu- meration of special classes of alternating permutations, and the connection between alternating permutations and the cd-index of the symmetric group. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday

Subfields: Algebra and Number Theory, Artificial Intelligence, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/2c062b3ebdc9a037495dafeb5119acfca9c9edd8