Title: Lehman Matrices
Speaker: Gerard Cornuejols
When: February 7, 12:30-13:30
Where: Porter Hall 125B
Abstract:
A pair of square $0,1$ matrices $A,B$ such that $AB^T=E+kI$ (where $E$ is the $n \times n$ matrix of all 1s and $k$ is a positive integer) are called {\em Lehman matrices}. These matrices figure prominently in Lehman’s seminal theorem on minimally nonideal matrices. There are two choices of $k$ for which this matrix equation is known to have infinite families of solutions. When $n=k^2+k+1$ and $A=B$, we get point-line incidence matrices of finite projective planes, which have been widely studied in the literature. The other case occurs when $k=1$ and $n$ is arbitrary, but very little is known in this case. This talk discusses this class of Lehman matrices and classifies them according to their similarity to circulant matrices. The work is joint with Betrand Guenin and Levent Tuncel.
