Two Poset Polytopes

@article{Stanley1986TwoPP,
  title={Two Poset Polytopes},
  author={Richard P. Stanley},
  journal={Discrete & Computational Geometry},
  year={1986},
  volume={1},
  pages={9-23}
}
Two convex polytopes, called the order polytope d)(P) and chain polytope <~(P), are associated with a finite poset P. There is a close interplay between the combinatorial structure of P and the geometric structure of E~(P). For instance, the order polynomial fl(P, m) of P and Ehrhart polynomial i(~9(P),m) of O(P) are related by f~(P,m+l)=i(d)(P),m). A "transfer map" then allows us to transfer properties of O(P) to W(P). In particular, we transfer known inequalities involving linear extensions… CONTINUE READING
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