, Volume 2, Issue 2, pp 193–198 | Cite as

About polytopes of valuations on finite distributive lattices

  • Hans Dobbertin


Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. We verify the conjecture of Geissinger that the extreme points of the convex polytope M(L)={v ∈ L : 0 ≤ v ≤ 1} are precisely the 0–1 valuations.

AMS (MOS) subject classifications (1980)

06A10 06D99 52A25 

Key words

Finite distributive lattices finite posets valuations convex polytopes extreme points 


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  1. 1.
    L. Geissinger (1981) The face structure of a poset polytope, Proceedings of the Third Caribbean Conference on Combinatorics and Computings, University of the West Indies, Cave Hill, Barbados, pp. 125–133.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Hans Dobbertin
    • 1
  1. 1.Institut für MathematikTU ClausthalClausthal-ZellerfeldWest Germany

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