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Restricted Addition and some Developments of the Erdős–Ginzburg–ziv Theorem
Author(s) -
Hennecart F.
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004534
Subject(s) - mathematics , modulo , abelian group , integer (computer science) , structured program theorem , discrete mathematics , combinatorics , computer science , programming language
Thanks to Szemerédi's theorem on sets with no long arithmetic progressions, an elementary trick is used here to show that for a given positive integer h and a given set U of residue classes modulo n with positive density, there exists a dense subset V of U ; that is, U / V is very small, such that the sumset hV is included in the restricted sumset h × U . The next step is to obtain information on the structure of V from Kneser's theorem on the sum of sets in an abelian group, and to use this for studying the structure of U itself. Finally, this idea is used in the paper to derive some new values of a function related to the Erdős–Ginzburg–Ziv theorem. 2000 Mathematics Subject Classification 05D05 (primary), 11B50 (secondary).