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About polytopes of valuations on finite distributive lattices

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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.

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  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.

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Communicated by A. Björner

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Dobbertin, H. About polytopes of valuations on finite distributive lattices. Order 2, 193–198 (1985).

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