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Large restricted sumsets in general Abelian groups

Author
Hamidoune, Y.O.; López, S.C.; Plagne, A.
Type of activity
Journal article
Journal
European journal of combinatorics
Date of publication
2013-11
Volume
34
Number
8
First page
1348
Last page
1364
DOI
https://doi.org/10.1016/j.ejc.2013.05.020 Open in new window
Abstract
Let A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect to S is defined as A¿SB = {a + b : a ¿ A, b ¿ Banda - b ¿ S} Let L S = max z ¿G| { (x, y) : x, y ¿ G, x + y = zandx - y ¿ S} |. A simple application of the pigeonhole principle shows that |A| + |B| > |G| + L S implies A¿SB = G. We then prove that if |A| + |B| = |G| + L S then |A¿SB| = |G| - 2|S|. We also characterize the triples of sets (A, B, S) such that |A| + |B| = |G| + L S and |A¿S...
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants

  • Hamidoune, Yayha Old  (author)
  • López Masip, Susana Clara  (author)
  • Plagne, Alain  (author)