On the cone of f-vectors of cubical polytopes

Ron M. Adin; Daniel Kalmanovich; Eran Nevo

On the cone of f-vectors of cubical polytopes

Ron M. Adin, Daniel Kalmanovich, Eran Nevo

Einstein Institute of Mathematics

Research output: Contribution to conference › Paper › peer-review

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.

Original language	American English
State	Published - 2018
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: 16 Jul 2018 → 20 Jul 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	16/07/18 → 20/07/18

Bibliographical note

Funding Information:
The authors thank Michael Joswig and Isabella Novik for helpful comments. The research of Adin was supported by an MIT-Israel MISTI grant. He also thanks the Israel Institute for Advanced Studies, Jerusalem, for its hospitality during part of the work on this paper. The research of Kalmanovich and Nevo was partially supported by Israel Science Foundation grant ISF-1695/15 and by grant 2528/16 of the ISF-NRF Singapore joint research program. This work was also partially supported by the National Science Foundation under Grant No. DMS-1440140, while Nevo was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester.

Publisher Copyright:
© FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Keywords

Cubical g-vector
Cubical polytope

Cite this

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title = "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.",

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AU - Kalmanovich, Daniel

AU - Nevo, Eran

N1 - Funding Information: The authors thank Michael Joswig and Isabella Novik for helpful comments. The research of Adin was supported by an MIT-Israel MISTI grant. He also thanks the Israel Institute for Advanced Studies, Jerusalem, for its hospitality during part of the work on this paper. The research of Kalmanovich and Nevo was partially supported by Israel Science Foundation grant ISF-1695/15 and by grant 2528/16 of the ISF-NRF Singapore joint research program. This work was also partially supported by the National Science Foundation under Grant No. DMS-1440140, while Nevo was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester. Publisher Copyright: © FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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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KW - Cubical polytope

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M3 - Paper

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T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

On the cone of f-vectors of cubical polytopes

Abstract

Conference

Bibliographical note

Keywords

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