Order

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

About polytopes of valuations on finite distributive lattices

  • Hans Dobbertin
Article

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations