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Rödl and Ruciński established Ramsey's theorem for random graphs. In particular, for fixed integers
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In general, random walks on fractal graphs are expected to exhibit anomalous behaviors, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach in 1982 conjectured that random walks on critical percolation, a prominent example of fractal graphs, exhibit mean field behavior; for instance, its spectral dimension is … |
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This talk will first introduce combinatorics on permutations and patterns, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given pattern, and the Guillemot-Marx algorithm for pattern detection using the notion now known as twin-width. I will then present a decomposition result: permutations avoiding a … |
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A classical problem in combinatorial geometry, posed by Erdős in 1946, asks to determine the maximum number of unit segments in a set of |
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