Reflexive polytopes arising from partially ordered sets and perfect graphs
- 77 Downloads
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.
KeywordsReflexive polytope Integer decomposition property Order polytope Stable set polytope Perfect graph Ehrhart \(\delta \)-polynomial Gröbner basis
Mathematics Subject Classification13P10 52B20
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.
- 7.Hibi, T.: Distributive lattices, affine semigroup rings and algebras with straightening laws, In: Nagata, M., Matsumura, H. (eds.) Commutative Algebra and Combinatorics, Advanced Studies in Pure Math., vol. 11, pp. 93–109. North-Holland, Amsterdam (1987)Google Scholar
- 14.Hibi, T., Matsuda, K., Tsuchiya, A.: Gorenstein Fano polytopes arising from order polytopes and chain polytopes. arXiv:1507.03221
- 16.Hibi, T., Tsuchiya, A.: Reflexive polytopes arising from perfect graphs. arXiv:1703.04410
- 21.Ohsugi, T.: Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes. J. Commut. Algebra (to appear). https://projecteuclid.org/euclid.jca/1465576138