Dr. Ezra Brown, 9 October, 2006

The Many Names of (7,3,1)

Abstract: This is a story about a single object, living in the world of discrete mathematics, that makes many connections. It is a difference set, a block design, a Steiner triple system, a finite projective plane, a complete set of orthogonal Latin squares, a doubly regular tournament, a skew-Hadamard matrix, a graph consisting of seven mutually adjacent hexagons drawn on the torus, a perfect single-error correcting code, and a solution to the Seven Hats Problem. We investigate these connections and get to know this object, commonly known as (7,3,1), and its many other names quite well.

Biographical Sketch:  Ezra (Bud) Brown has degrees from Rice and Louisiana State, and has been at Virginia Tech since 1969, where he is currently Alumni Distinguished Professor of Mathematics. His research interests include number theory, graph theory and combinatorics, and he particularly enjoys discovering connections between apparently unrelated areas of mathematics.          He enjoys singing (everything from grand opera to rock'n'roll), playing jazz piano, working with students who are engaged in research, and talking about his granddaughter Phoebe Rose. With his wife Jo's help, he has become a fairly tolerable gardener. He occasionally bakes biscuits for his students.