### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu
**Nathan Fox**, Rutgers University, fox {at} math [dot] rutgers [dot] edu)

Title: Noncommutative Catalan numbers

Speaker: **Vladimir Retakh**, Rutgers Universtiy

Date: Thursday, October 27, 2016 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We introduce and study noncommutative Catalan "numbers" as Laurent polynomials in free variables and related theory of noncommutative binomial coefficients. We also study their (commutative and noncommutative) specializations, relate them with Garsia-Haiman (q,t)-versions, and establish total positivity of the corresponding Hankel matrices. This is my work in progress with Arkady Berenstein from Univ. of Oregon.

See: http://www.math.rutgers.edu/~nhf12/expmath/