Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Edge-matching - Where Are the Theorems?

Speaker: **Arthur DuPre**, Rutgers University

Date: Thursday, October 15, 2009 5:00pm

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

Abstract:

MacMahon discovered early last century that the set of triangles whose edges are colored with at most 4 colors, 24 in all, could be arranged into a hexagon in which each pair of adjacent edges are the same color (see http://math.rutgers.edu/~dupre/puzzles/hextriangles.gif). Similarly, he also showed that the 24 possible squares colored with at most 3 colors could be arranged into either a 3x8 rectangle or a 4x6 one, edges matching as above. A few months ago, I began to use these triangles and squares and certain subsets to tile the surfaces of various polyhedra. My work has so far been by hand, but Jacques Haubrich of the Netherlands and Peter Esser in England have been kind enough to use their computer skills to answer some of the questions I have posed to them.

Most of the results in this subject have been gained by use of computer programs, but it is a challenging idea to see some order in all this seemingly chaotic landscape, and this talk will be a description of my tantalizingly uncussessful attempts to do this.