Sieve methods in combinatorics |
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Authors: | Yu-Ru Liu M Ram Murty |
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Institution: | a Department of Pure Mathematics, University of Waterloo, Waterloo, Ont., Canada, N2L 3G1 b Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6 |
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Abstract: | We develop the Turán sieve and a ‘simple sieve’ in the context of bipartite graphs and apply them to various problems in combinatorics. More precisely, we provide applications in the cases of characters of abelian groups, vertex-colourings of graphs, Latin squares, connected graphs, and generators of groups. In addition, we give a spectral interpretation of the Turán sieve. |
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Keywords: | 05A05 11N35 |
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