### 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:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Greatest Common Divisors of Specialized Schur Functions and Generalized Parking Spaces

Speaker: ** Soichi Okada**, Nagoya University

Date: Thursday, April 17, 2014 5:00pm

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

Abstract:

Given two positive integers n and k, we find the greatest
common divisor of the special values s_λ(1^k) of Schur
functions, where λ runs over all partitions of n.
As an application, we determine when generalized parking spaces
exist for the symmetric groups. We also discuss the greatest
common divisor of the principally specialized Schur functions
and present a conjecture on the unimodality of the coefficients
of certain polynomials obtained as a quotient of the principal
specializations.

See: http://www.math.rutgers.edu/~russell2/expmath/