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:

Drew Sills, Rutgers University, asills {at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Chess tableaux and chess problems

Speaker: Timothy Chow, Center for Communication Research (Princeton)

Date: Thursday, November 30, 2006 5:00pm

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

Abstract:

A chess tableau is a standard Young tableau (SYT) in which orthogonally adjacent entries have opposite parity. Remarkably, the number of 3xn chess tableaux is the same as the number of 3x(n-1) nonconsecutive tableaux (SYT in which i and i+1 never appear in the same row), the Charney-Davis statistic of a 3xn shape, and the number of Baxter permutations of n. A WZ-style proof of at least some of these facts should be possible in principle, but the naive approaches we have tried have crashed the computer. In the last part of the talk we present two chess problems that are related to chess tableaux.