Zero-one matrices with zero trace

Abstract

General existence conditions for an n × n zero-one matrix having given row and column sums and zero trace consist of a set of 2n − 1 inequalities. These are shown to simplify to the following set of n inequalities in case the row sums ai and column sums bi satisfy a1 ≥ … ≥ an, b1 ≥ … bn: where is the number of ai such that i < j and ai ≤ j − 1 plus the number of ai such that i < j and ai ≥ j . © 1960 by Pacific Journal of Mathematics.