Discrete & Computational Geometry

, Volume 1, Issue 1, pp 9–23 | Cite as

Two poset polytopes

  • Richard P. Stanley


Two convex polytopes, called theorder polytope ϑ(P) andchain polytope ℒ(P), are associated with a finite posetP. There is a close interplay between the combinatorial structure ofP and the geometric structure of ϑ(P). For instance, the order polynomial Ω(P, m) ofP and Ehrhart polynomiali(ϑ(P),m) of ϑ(P) are related by Ω(P, m+1)=i(ϑ(P),m). A “transfer map” then allows us to transfer properties of ϑ(P) to ℒ(P). In particular, we transfer known inequalities involving linear extensions ofP to some new inequalities.


Discrete Comput Geom Linear Extension Convex Polytopes Mixed Volume Abstract Simplicial Complex 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Richard P. Stanley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridge

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