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Finite modules over non-semisimple group rings |
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| Authors: | |
| Institution: | (1) Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden;(2) Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland;(3) Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland |
| Abstract: | LetG be a fixed graph and letX G be the number of copies ofG contained in the random graphG(n, p). We prove exponential bounds on the upper tail ofX G which are best possible up to a logarithmic factor in the exponent. Our argument relies on an extension of Alon’s result about the maximum number of copies ofG in a graph with a given number of edges. Similar bounds are proved for the random graphG(n, M) too. Research of the second author supported by KBN grant 2 P03A 027 22. Research of the third author supported by KBN grant 2 P03A 15 23. |
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