On the cone of $f$-vectors of cubical polytopes
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- by Ron M. Adin, Daniel Kalmanovich and Eran Nevo PDF
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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.References
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Additional Information
- Ron M. Adin
- Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
- Email: radin@math.biu.ac.il
- Daniel Kalmanovich
- Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
- MR Author ID: 984250
- Email: daniel.kalmanovich@gmail.com
- Eran Nevo
- Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
- MR Author ID: 762118
- Email: nevo.eran@gmail.com
- Received by editor(s): May 18, 2018
- Published electronically: January 18, 2019
- Additional Notes: The research of the first author 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 the second and third authors 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 the third author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester. - Communicated by: Patricia Hersh
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1851-1866
- MSC (2010): Primary 05--XX, 52--XX; Secondary 52B05
- DOI: https://doi.org/10.1090/proc/14380
- MathSciNet review: 3937665