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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convex polytopes all of whose reverse lexicographic initial ideals are squarefree


Authors: Hidefumi Ohsugi and Takayuki Hibi
Journal: Proc. Amer. Math. Soc. 129 (2001), 2541-2546
MSC (2000): Primary 13P10, 52B20
Published electronically: January 18, 2001
MathSciNet review: 1838375
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Abstract:

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a $(0,1)$-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed $(0,1)$-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of perfect graphs.


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Additional Information

Hidefumi Ohsugi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560–0043, Japan
Email: ohsugi@math.sci.osaka-u.ac.jp

Takayuki Hibi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560–0043, Japan
Email: hibi@math.sci.osaka-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05853-1
PII: S 0002-9939(01)05853-1
Keywords: Compressed polytopes, initial ideals, unimodular triangulations
Received by editor(s): November 3, 1999
Received by editor(s) in revised form: January 17, 2000
Published electronically: January 18, 2001
Additional Notes: The first author is supported by JSPS Research Fellowship for Young Scientists.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society