#### Title

#### Date of Original Version

7-29-2006

#### Type

Article

#### Abstract or Description

A pair of square 0, 1 matrices A,B such that AB^{T} = E + kI (where E is the n × n matrix of all 1s and k is a positive integer) are called 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 paper studies this class of Lehman matrices and classifies them according to their similarity to circulant matrices.

#### DOI

10.1016/j.jctb.2008.06.009

#### Published In

Journal of Combinatorial Theory, Series B, 99, 3, 531-556.