### 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: The Red Dot Problem: Squares Containing No Subsquares

Speaker: **Neil J. A. Sloane**, Rutgers University and The OEIS Foundation

Date: Thursday, April 21, 2016 5:00pm

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

Abstract:

Every few days a number sequence is submitted to the OEIS which is so lovely that one says "if only I had time to work on this". This talk is about one such sequence that I did work on, with a lot of help from Warren Smith. How many cells of an n X n grid can you color red so that no four of them form a square with sides parallel to the sides of the grid? The names Heinrich Ludwig, Waclaw Sierpinski, Endre Szemerédi, Furstenberg and Katznelson, Felix Behrend, and of course Robert Louis Stevenson will be mentioned.

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