Unimodality of f-vectors of cyclic polytopes

László Major

Published 2011-06-22, updated 2011-07-25Version 2

Cyclic polytopes are generally known for being involved in the Upper Bound Theorem, but they have another extremal property which is less well known. Namely, the special shape of their f-vectors makes them applicable to certain constructions to present non-unimodal convex polytopes. Nevertheless, the f-vectors of cyclic polytopes themselves are unimodal.