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Hypermetric Spaces and the Hamming Cone

Published online by Cambridge University Press:  20 November 2018

David Avis
David Avis*
Affiliation:
McGill University, Montreal, Quebec
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We denote by d = (d12, …, d1n, d23, …, dn-1,n) a vector of distances between n points. Such a vector d is called a metric if it satisfies the triangle inequalities

(1)

The set of all metrics on n points forms a convex polyhedral cone, the extremal properties of which are discussed in [4]. We will be concerned with a sub-cone that is spanned by metrics of the form

(2)

where t ≧ 0, V is a proper subset of {1, 2, …, n}; and the symbol ⊥ is used for “exclusive or”: i ⊥ j ∈ V means i ∈ V, j ∉ V or i ∉ V,j∉ V.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 795 - 802
Copyright
Copyright © Canadian Mathematical Society 1981

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