Lopsided sets and orthant-intersection by convex sets
James F. Lawrence · Pacific Journal of Mathematics · 1983
Given a subset L of the 2 d closed orthants in ^-dimensional Euclidean space, is there a convex set K which intersects those closed orthants in L, while missing those not in L? A strong combinatorial condition on L, which is necessary for the existence of such a convex set, is exhibited.This condition is studied and its close connections with the theory of oriented matroids are examined.The sets L satisfying this conditionthe "lopsided" sets -have a rich combinatorial structure which can be exploited in the study of convex sets and systems of linear inequalities.