Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424355 | European Journal of Combinatorics | 2013 | 17 Pages |
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 Aâ§SB={a+b:aâA,bâBandaâbâS}. Let LS=maxzâG|{(x,y):x,yâG,x+y=zandxâyâS}|. A simple application of the pigeonhole principle shows that |A|+|B|>|G|+LS implies Aâ§SB=G. We then prove that if |A|+|B|=|G|+LS then |Aâ§SB|â¥|G|â2|S|. We also characterize the triples of sets (A,B,S) such that |A|+|B|=|G|+LS and |Aâ§SB|=|G|â2|S|. Moreover, in this case, we also provide the structure of the set Gâ(Aâ§SB).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yahya Ould Hamidoune, Susana-Clara López, Alain Plagne,