Towards a classification of transitive group actions on finite metric spaces

DOI10.1016/0001-8708(89)90008-XzbMath0683.54041MaRDI QIDQ1824899

Andreas W. M. Dress

Publication date: 1989

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite metric spacesquasi-isometryinjective hullG- invariant metricinvariant under left multiplicationsets of maximal dimension facetstransitive groups of isometries

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Geometric group theory (20F65) Transformation groups and semigroups (topological aspects) (54H15) Special maps on metric spaces (54E40) Other problems of combinatorial convexity (52A37) Polytopes and polyhedra (52Bxx)

Related Items (9)

On classification of finite metric spaces ⋮ The polytopal structure of the tight-span of a totally split-decomposable metric ⋮ Injective envelopes of transition systems and Ferrers languages ⋮ An explicit computation of the injective hull of certain finite metric spaces in terms of their associated Buneman complex ⋮ Optimal realizations and the block decomposition of a finite metric space ⋮ Injective envelope of graphs and transition systems ⋮ The coherency index ⋮ INJECTIVE HULLS OF CERTAIN DISCRETE METRIC SPACES AND GROUPS ⋮ The tight span of an antipodal metric space. I: combinatorial properties

Cites Work

• Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
• Six theorems about injective metric spaces
• Abstract length functions in groups
• Length Functions in Groups.

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