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arXiv · 1801.00163

On the cone of $f$-vectors of cubical polytopes

Ron M. Adin·Daniel Kalmanovich·Eran Nevo
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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.

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Ron M. Adin, Daniel Kalmanovich, Eran Nevo. 2018-05-18. On the cone of $f$-vectors of cubical polytopes. https://arxiv.org/abs/1801.00163

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