About polytopes of valuations on finite distributive lattices
type: Item
instance of: scholarly article
title: About polytopes of valuations on finite distributive lattices
zbMATH Open document ID: 0577.06013
DOI: 10.1007/BF00334856
author: Hans Dobbertin
published in: Order
publication date: 1985-01-01T00:00:00Z
review text: Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. The author verifies the conjecture of \textit{L. Geissinger} [Combinatorics and computing, Proc. 3rd Caribb. Conf., Cave Hill/Barbados 1981, 125-133 (1981; Zbl 0523.06005)] that the extreme points of the convex polytope \(M(L)=\{v\in V(L):\) \(0\leq v\leq 1\}\) are precisely the 0-1 valuations.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 3922724
zbMATH Keywords: finite distributive lattice
zbMATH Keywords: valuations
zbMATH Keywords: extreme points
zbMATH Keywords: convex polytope
MaRDI profile type: Publication
cites work: Q3674721
Recommended article: Valuations on Lattice Polytopes
Recommended article: Valuations on lattice polytopes
Recommended article: A brief introduction to valuations on lattice polytopes
Recommended article: Minkowski valuations on lattice polytopes
Recommended article: Valuations on complemented lattices
Recommended article: Enumerating faces of complexes and valuations on distributive lattices
Recommended article: Q3629318
Recommended article: Q5636938
Recommended article: Valuative invariants for polymatroids
Recommended article: Q4591296
description: scientific article; zbMATH DE number 3922724