MIT Combinatorics Seminar
Alternating Permutations
Richard Stanley (Massachusetts Institute of Technology)
Friday, May 5, 2006 4:30 PM Building 2 Room 105
ABSTRACT

A permutation a_1 a_2 ... a_n of integers is *alternating*
if a_1 > a_2 < a_3 > a_4 < ... After a brief survey of this subject we
will discuss two new directions of research. (1) The distribution of
the length of the longest alternating subsequence of a permutation of
1,2,...,n, analogous to the theory of longest increasing
subsequences. (2) The use of symmetric functions to enumerate various
classes of alternating permutations of 1,2,...,n, such as those whose
inverse is also alternating, or those with a given cycle type.


