Polytopes from Posets

Poset から作られる多面体としては, まず Stanley [Sta86] により定義された chain polytope と order polytope がある。その変種も色々定義されている。

• chain polytope と order polytope
• marked chain polytope と marked order polytope [ABS11]
• chain-order polytope [Hib+]
• marked chain-order polytope [FF]
• enriched order polytope tol enriched chain polytope [OT]

他に目についたものを挙げると, 次のようになる。

• poset associahedron [Gal]
• linear order polytope [BKG99; CSS; EY]
• partial order polytope [Fio03]

References

[ABS11]

Federico Ardila, Thomas Bliem, and Dido Salazar. “Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg polytopes as marked poset polytopes”. In: J. Combin. Theory Ser. A 118.8 (2011), pp. 2454–2462. arXiv: 1008 . 2365. url: http://dx.doi.org/10.1016/j.jcta.2011.06.004.

[BKG99]

G. Bolotashvili, M. Kovalev, and E. Girlich. “New facets of the linear ordering polytope”. In: SIAM J. Discrete Math. 12.3 (1999), pp. 326–336. url: https://doi.org/10.1137/S0895480196300145.

[CSS]

Ilya Chevyrev, Dominic Searles, and Arkadii Slinko. On the Number of Facets of Polytopes Representing Comparative Probability Orders. arXiv: 1103.3938.

[EY]

Adolfo R. Escobedo and Romena Yasmin. Derivations of large classes of facet-defining inequalities of the weak order polytope using ranking structures. arXiv: 2008.03799.

[FF]

Xin Fang and Ghislain Fourier. Marked chain-order polytopes. arXiv: 1508.02232.

[Fio03]

Samuel Fiorini. “A combinatorial study of partial order polytopes”. In: European J. Combin. 24.2 (2003), pp. 149–159. url: https://doi.org/10.1016/S0195-6698(03)00009-X.

[Gal]

Pavel Galashin. Poset associahedra. arXiv: 2110.07257.

[Hib+]

Takayuki Hibi, Nan Li, Teresa Xueshan Li, Lili Mu, and Akiyoshi Tsuchiya. Order-Chain Polytopes. arXiv: 1504.01706.

[OT]

Hidefumi Ohsugi and Akiyoshi Tsuchiya. Enriched order polytopes and Enriched Hibi rings. arXiv: 1903.00909.

[Sta86]

Richard P. Stanley. “Two poset polytopes”. In: Discrete Comput. Geom. 1.1 (1986), pp. 9–23. url: http://dx.doi.org/10.1007/BF02187680.