INTEGRAL EXTREME POINTS
STANFORD UNIV CA OPERATIONS RESEARCH HOUSE
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It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1. This provides a short proof of the Hoffman- Kruskal theorem characterizing unimodular matrices, i.e., matrices in which the determinant of each nonsingular submatrix is plus or minus 1. Their theorem is that if A is integral, then A is unimodular if and only if the extreme points of the set of nonnegative solutions to Ax or b are integral for all integral b.
- Operations Research