Hypergraph polytopes

Polytopes Determined by Hypergraph Classes

DEFINITION 1.1. For a finite subset Xc IR n + 1 we say that D is the dominating set of X if (a) Dc X, (b) for all x E X there exist dlo d2 , ••• , dj ED and positive real numbers alo"" aj so that L. a, = I and L. ajdj dominates x, (c) D is minimal with respect to these properties. The elements of D are called dominating vertices. It is not hard to see that D consists of exactly those vertices o...

Hypercube Related Polytopes

Body centered structures are used as seeds for a variety of structures of rank 3 and higher. Propellane based structures are introduced and their design and topological properties are detailed.

Gorenstein Fano Polytopes Arising from Order Polytopes and Chain Polytopes

Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...

Hypergraph Rewriting

In their pioneering paper [KB70], Knuth and Bendix showed that con uence (or, equivalently, the Church-Rosser property) is decidable for terminating term rewriting systems. It su ces to compute all critical pairs t s ! u of rewrite steps in which s is the superposition of the left-hand sides of two rules, and to check whether t and u reduce to a common term. This procedure is justi ed by the so...

Hypergraph Codes