BINDING CONSTRAINTS AND HELLY NUMBERS
Alan J. Hoffman · Annals of the New York Academy of Sciences · 1979
S ummary Starting with axioms for an abstract intersectional system, we define the Helly number., Scarf number , and binding constraint number of such a system. The last concept is based on a definition of a mathematical programming problem in the system. From these definitions, we deduce (1) Bell's theorem that a collection of half spaces contains a point of ß n if the intersection of every subset of 2 n of the half spaces does, and (2) Scarf's theorem that an integer programming problem on z n has at most 2 n — 1 binding constraints. Our arguments use coordinates only at the last moment.