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 | References | Similar Articles | Additional Information

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a -polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed -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:
https://doi.org/10.1090/S0002-9939-01-05853-1

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