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Journal of Algebraic Combinatorics

, Volume 49, Issue 1, pp 69–81 | Cite as

Reflexive polytopes arising from partially ordered sets and perfect graphs

  • Takayuki Hibi
  • Akiyoshi TsuchiyaEmail author
Article

Abstract

Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite partially ordered sets are known. In the present paper, we will generalize this result. In fact, by virtue of the algebraic technique on Gröbner bases, new classes of reflexive polytopes with the integer decomposition property coming from the order polytopes of finite partially ordered sets and the stable set polytopes of perfect graphs will be introduced. Furthermore, the result will give a polyhedral characterization of perfect graphs. Finally, we will investigate the Ehrhart \(\delta \)-polynomials of these reflexive polytopes.

Keywords

Reflexive polytope Integer decomposition property Order polytope Stable set polytope Perfect graph Ehrhart \(\delta \)-polynomial Gröbner basis 

Mathematics Subject Classification

13P10 52B20 

Notes

Acknowledgements

The authors would like to thank anonymous referees for reading the manuscript carefully. Akiyoshi Tsuchiya partially supported by Grant-in-Aid for JSPS Fellows 16J01549.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan

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