Restricted sumsets and a conjecture of Lev
| dc.creator | Pan, Hao | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2005-03-27 | |
| dc.date | 2006-10-29 | |
| dc.date.accessioned | 2026-07-07T06:39:40Z | |
| dc.date.available | 2026-07-07T06:39:40Z | |
| dc.description | Let A,B,S be finite subsets of an abelian group G. Suppose that the restricted sumset C={a+b: a in A, b in B, and a-b not in S} is nonempty and some c in C can be written as a+b with a in A and b in B in at most m ways. We show that if G is torsion-free or elementary abelian then |C|\geq |A|+|B|-|S| -m. We also prove that |C|\geq |A|+|B|-2|S|-m if the torsion subgroup of G is cyclic. In the case S={0} this provides an advance on a conjecture of Lev. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503620 | |
| dc.identifier | http://arxiv.org/abs/math/0503620 | |
| dc.identifier | Israel J. Math. 154(2006), 21-28 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101160 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05A05; 11B75; 11P99; 20D60 | |
| dc.title | Restricted sumsets and a conjecture of Lev | |
| dc.type | text |