Séminaire Lotharingien de Combinatoire, 80B.85 (2018), 12 pp.
Ron M. Adin, Daniel Kalmanovich, and Eran Nevo
On the Cone of f-Vectors of Cubical Polytopes
Abstract.
What is the minimal closed cone containing all f-vectors of cubical d-polytopes?
We construct cubical polytopes showing that this cone, expressed in the cubical g-vector coordinates, contains the nonnegative g-orthant,
thus verifying one direction of the Cubical Generalized Lower Bound Conjecture of Babson, Billera and Chan. Our polytopes also show that a natural cubical analogue of the simplicial Generalized Lower Bound Theorem does not hold.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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