## Profile polytopes of some classes of families

- Dániel Gerbner
- Combinatorica
- 2013

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… (More)