BINDING CONSTRAINTS AND HELLY NUMBERS
- 1 May 1979
- journal article
- Published by Wiley in Annals of the New York Academy of Sciences
- Vol. 319 (1) , 284-288
- https://doi.org/10.1111/j.1749-6632.1979.tb32803.x
Abstract
Summary: 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 ßn if the intersection of every subset of 2n of the half spaces does, and (2) Scarf's theorem that an integer programming problem on zn has at most 2n— 1 binding constraints. Our arguments use coordinates only at the last moment.Keywords
This publication has 2 references indexed in Scilit:
- A Theorem Concerning the Integer LatticeStudies in Applied Mathematics, 1977
- Helly’s theorem and its relativesPublished by American Mathematical Society (AMS) ,1963