Cyclohedron and Kantorovich–Rubinstein Polytopes

Cyclohedron and Kantorovich–Rubinstein Polytopes We show that the cyclohedron (Bott–Taubes polytope) $$W_n$$ W n arises as the polar dual of a Kantorovich–Rubinstein polytope $$KR(\rho )$$ K R ( ρ ) , where $$\rho $$ ρ is an explicitly described quasi-metric (asymmetric distance function) satisfying strict triangle inequality. From a broader perspective, this phenomenon illustrates the relationship between a nestohedron $$\Delta _{{\widehat{\mathcal {F}}}}$$ Δ F ^ (associated to a building set $${\widehat{\mathcal {F}}}$$ F ^ ) and its non-simple deformation $$\Delta _{\mathcal {F}}$$ Δ F , where $$\mathcal {F}$$ F is an irredundant or tight basis of $${\widehat{\mathcal {F}}}$$ F ^ (Definition 21). Among the consequences are a new proof of a recent result of Gordon and Petrov (Arnold Math. J. 3(2):205–218, 2017) about f-vectors of generic Kantorovich–Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive root polytopes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Cyclohedron and Kantorovich–Rubinstein Polytopes

Loading next page...
 
/lp/springer_journal/cyclohedron-and-kantorovich-rubinstein-polytopes-fdrgd0lRVH
Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
D.O.I.
10.1007/s40598-018-0083-4
Publisher site
See Article on Publisher Site

Abstract

We show that the cyclohedron (Bott–Taubes polytope) $$W_n$$ W n arises as the polar dual of a Kantorovich–Rubinstein polytope $$KR(\rho )$$ K R ( ρ ) , where $$\rho $$ ρ is an explicitly described quasi-metric (asymmetric distance function) satisfying strict triangle inequality. From a broader perspective, this phenomenon illustrates the relationship between a nestohedron $$\Delta _{{\widehat{\mathcal {F}}}}$$ Δ F ^ (associated to a building set $${\widehat{\mathcal {F}}}$$ F ^ ) and its non-simple deformation $$\Delta _{\mathcal {F}}$$ Δ F , where $$\mathcal {F}$$ F is an irredundant or tight basis of $${\widehat{\mathcal {F}}}$$ F ^ (Definition 21). Among the consequences are a new proof of a recent result of Gordon and Petrov (Arnold Math. J. 3(2):205–218, 2017) about f-vectors of generic Kantorovich–Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive root polytopes.

Journal

Arnold Mathematical JournalSpringer Journals

Published: Apr 9, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off