On the exterior algebra method applied to restricted set addition |
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Authors: | Gyula Károlyi Roland Paulin |
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Institution: | 1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia;2. Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland |
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Abstract: | In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A of the p-element group Z/pZ (where p is a prime), at least min{p,m|A|−m2+1} different elements of the group can be written as the sum of m different elements of A. In this note we present an easily accessible simplified version of their proof for the case m=2, and explain how the method can be applied to obtain the corresponding inverse theorem. |
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