منابع مشابه
Hypermetric Spaces and the Hamming Cone
where / ^ 0, F is a proper subset of {1, 2, . . . , n) and the symbol 1_ is used for "exclusive or": i JL j £ V means i G V, j £ V or i (? V,j(z V. The metrics (2) are extreme rays of the metric cone and are called Hamming rays. The convex hull of these rays is called the Hamming cone Hn and we call d Hamming, if d Ç Hn. Such metrics are also called L-embeddable (e.g., [2]) or addressable (e.g....
متن کاملThe hypermetric cone is polydedral
The hypermetric cone Hn is the cone in the space R n(n1)/2 of all vectors d = (dij) 1 <i< j <_ n satisfying the hypermetric inequalities: El<_i<j<n zjzjdij ~0 for all integer vectors z in Z n with E l < i < n zi = 1. We explore connections of the hypermetric cone with quadratic forms and the geometry of numbers (empty spheres and L-polytopes in lattices). As an application, we show that the hyp...
متن کاملThe Hypermetric Cone on Seven Vertices
The hypermetric cone HY Pn is the set of vectors (dij)1≤i<j≤n satisfying the inequalities
متن کاملThe Hypermetric Cone on 8 Vertices and Some Generalizations
The lists of facets – 298, 592 in 86 orbits – and of extreme rays – 242, 695, 427 in 9, 003 orbits – of the hypermetric cone HY P8 are computed. The first generalization considered is the hypermetric polytope HY PPn for which we give general algorithms and a description for n ≤ 8. Then we shortly consider generalizations to simplices of volume higher than 1, hypermetric on graphs and infinite d...
متن کاملThe classification of finite connected hypermetric spaces
A finite distance space X , d d : X 2 --,7/ is hypermetric (of negative type) if axay d(x, y) < 0 for all integral sequences {axlx ~ X} that sum to 1 (sum to 0). X, d is connected if the set {(x, y)ld(x, y) = 1, x, y ~ X} is the edge set for a connected graph on X, and graphical if d is the path length distance for this graph. Then we prove Theorem 1. A connected space X, d has negative type if...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1981
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1981-061-5