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]



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


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.


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


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.


Pavel Galashin. Poset associahedra. arXiv: 2110.07257.


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


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


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