Geodesic
On the Cone of f-Vectors of Cubical Polytopes
Séminaire lotharingien de combinatoire, 80B (2018)

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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. 

@article{SLC_2018_80B_a84,
     author = {Ron M. Adin and Daniel Kalmanovich, and Eran Nevo},
     title = {On the {Cone} of {f-Vectors} of {Cubical} {Polytopes}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a84/}
}
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%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a84/
%F SLC_2018_80B_a84
Ron M. Adin; Daniel Kalmanovich,; Eran Nevo. On the Cone of f-Vectors of Cubical Polytopes. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a84/