zbMATH — the first resource for mathematics

The width-length inequality and degenerate projective planes. (English) Zbl 0747.05063
Polyhedral combinatorics, Proc. Workshop, Morristown/NJ (USA) 1989, DIMACS, Ser. Discret. Math. Theor. Comput. Sci. 1, 101-105 (1990).
[For the entire collection see Zbl 0722.00003.]
Width-length systems were defined in A. Lehman [(*) Math. Program. 17, 403-417 (1979; Zbl 0418.90040)] as underpinning for resistor network inequalities. These inequalities yield realizability constraints on piecewise linear switch-resistor networks. Unexpectedly the width-length theory also leads to design and integer programming results. One of these is proven here. A consequence, mentioned in the foreword of A. Lehman [(*)], is that the degenerate projective planes are the only minimal matrices requiring unequal weights.

05C65 Hypergraphs
94C15 Applications of graph theory to circuits and networks
90C10 Integer programming