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, Volume 2, Issue 2, pp 193–198

About polytopes of valuations on finite distributive lattices

  • Hans Dobbertin
Article
  • 39 Downloads

Abstract

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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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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