### 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: Computer-assisted bijectification of algebraic proofs

Speaker: **Nathaniel Shar**, Rutgers University

Date: Thursday, October 24, 2013 2:00pm

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

Abstract:

If a(n) is the sum of the cubes of the entries on the nth row of Pascal'a triangle, then (n+1)^2 a(n) = (7n^2 - 7n + 2)a(n-1) + 8(n-1)^2a(n-2). It seems challenging for a human to find a bijective proof of this, but a computer can do it, with a little help. I'll show you a real live bijection, implemented of course by the computer, that proves this identity, and describe a method that might help computers bijectify other difficult identities.

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