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- Title
Relation Between the Kendall and Spearman Coefficients and Concordance Graphs.
- Authors
Plakhov, A.
- Abstract
A pair of linear orders L and L ′ on an n-element set V is called a concordance pair if the Kendall and Spearman correlation measures between L and L′' coincide. A graph is said to be concordance if it has the same number of induced three-vertex one-edged subgraphs as induced three-vertex two-edged subgraphs. It is known (see [2]) that (L, L′') is a concordance pair if and only if the comparability graph of a partially ordered set (V, L fl L′') is a concordance graph. In this paper, we estimate the portion of concordance pairs among all possible pairs of linear orders on V and the portion of concordance graphs among all graphs with the vertex set V. In both cases, the answer is O(n_-⅓), n → ∞ The results were obtained by methods of probability theory.
- Subjects
PARTIALLY ordered sets; CONCORDANCES (Topology); LINEAR orderings; FREE probability theory; MATHEMATICS
- Publication
Journal of Mathematical Sciences, 2004, Vol 120, Issue 1, p988
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1023/B:JOTH.0000013561.71027.04