Long Arithmetic Progressions in Sum-Sets and the Number x-Sum-Free Sets |
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| Authors: | Szemeredi E; Vu V H |
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| Institution: | Computer Science Department, Rutgers University 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. E-mail: szemered{at}cs.rutgers.edu
Department of Mathematics, University of California at San Diego La Jolla, CA 92093-0112, USA. E-mail: vanvu{at}ucsd.edu http://www.math.ucsd.edu/~vanvu/ |
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| Abstract: | In this paper we obtain optimal bounds for the length of thelongest arithmetic progression in various kinds of sum-sets.As an application, we derive a sharp estimate for the numberof sets A of residues modulo a prime n such that no subsum ofA equals x modulo n, where x is a fixed residue modulo n. 2000Mathematics Subject Classification 05A16, 11B25, 11P32. |
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| Keywords: | long arithmetic progression sum-set Freiman inverse theorem sum-free set |
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