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Convex polytopes all of whose reverse lexicographic initial ideals are squarefree
Author(s):
Hidefumi
Ohsugi;
Takayuki
Hibi
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2541-2546.
MSC (2000):
Primary 13P10, 52B20
Posted:
January 18, 2001
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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  -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.
References:
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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:
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
Posted:
January 18, 2001
Additional Notes:
The first author is supported by JSPS Research Fellowship for Young Scientists.
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2001,
American Mathematical Society
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