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A note on the similarity depth

โœ Scribed by G. Rozenberg; R. Verraedt


Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
220 KB
Volume
4
Category
Article
ISSN
0166-218X

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๐Ÿ“œ SIMILAR VOLUMES


A note on similarity relations
โœ Volker Strehl ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 287 KB

A simple proof is given for the fact that the number of nonsingular similarity relations on (1,2,... n), for which the transitive closure consists of k blocks, equals ("\*;'\_i-') -(2"-fh -'), 1, =G k s n/2. In particular, this implies a recent result of Shapiro about Catalan numbers and Fine's Jequ

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The so-called universal sequence that was discovered by Metropolis, [4], exhibits self-organization and self-similarity when its sequence of LR-patterns is translated into numerical values and depicted in a two-dimensional phase-portrait. This paper shows how this self-organization arises.

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This note presents a measure of similarity between connected nodes in terms of centrality based on Euclidean distances, and compares it to 'assortative mixing' [Newman, M.E.J., 2002. Assortative mixing in networks. Physical Review Letters 89, 208701], which is based on Pearson correlation coefficien