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# Tag Archives: homogeneous

## History of the Random Graph

That wonderful object, the countable random graph, was first considered by Erdős and Rényi in their paper on “Asymmetric graphs” in 1963. After proving that a large random finite graph (edges chosen independently with probability 1/2) has (with high probability) … Continue reading

Posted in exposition, history
Tagged back-and-forth, Cantor, Erdos, Fraisse, homogeneous, Huntington, Rado, Renyi, universal, Urysohn
7 Comments

## Almost highly transitive

I want to discuss a concept I have known about for quite a long time, but never found any real use for. Suggestions welcome! Highly transitive groups A permutation group is n-transitive if it has a single orbit on the … Continue reading

Posted in Uncategorized
Tagged generic, Henson's graph, homogeneous, multiorders, orders, Petrov-Vershik measure, random graph, universal
1 Comment

## Permutation groups and regular semigroups, 2

João Araújo and I have been working together this week, and the paper, which I discussed here, is nearly ready to submit, after we managed a couple of quite significant improvements. I’d like to draw attention to a couple of … Continue reading

Posted in mathematics, open problems
Tagged homogeneous, Livingstone, regular semigroups, set-transitive, universal transversal property, Wagner
7 Comments