University at Albany, SUNY

College of Arts and Sciences
Department of Mathematics and Statistics

Second Annual Maheshwari Colloquium

On Friday, April 12, 2013, the Department of Mathematics and Statistics at the University at Albany, SUNY, will host its second Maheshwari Colloquium, endowed in honor of Man Mohan and Asha Devi Maheshwari by Raj Maheshwari, ’83.

Photo of Richard P. StanleyThe speaker will be Richard P. Stanley from Massachusetts Institute of Technology, and the title of his lecture will be:

“Alternating Permutations.”

Abstract. A permutation \( a_1, a_2, \dotsc, a_n \) of \( 1, 2, \dotsc, n \) is called alternating if \( a_1 \gt a_2 \lt a_3 \gt a_4 \lt \dotsb \). The number of alternating permutations of \( 1, 2, \dotsc, n \) is denoted \( E_n \) and is called an Euler number. The most striking result about alternating permutations is the generating function \[ \sum_{n\geq 0} E_n \frac{x^n}{n!} = \sec x + \tan x , \] found by Désiré André in 1879. We will discuss this result and how it leads to the subject of “combinatorial trigonometry.” We will then survey some further aspects of alternating permutations, including some other objects that are counted by \( E_n \), the use of the representation theory of the symmetric group to count certain classes of alternating permutations, and the statistical properties of the longest alternating subsequence of a random permutation.

The colloquium will begin at 3:30 p.m. in the D’Ambra Auditorium of the Life Sciences Research Building (directions).
Refreshments will be served from 2:45 p.m. and there will be a light reception starting at 5 p.m., both just outside the auditorium.

For more information, please feel free to contact the organizers, Cristian Lenart, Marco Varisco, and Joshua Isralowitz.


Last year’s Inaugural Maheshwari Colloquium.