Extensions of the Moser-Scherck-Kemperman-Wehn Theorem
| dc.creator | Hamidoune, Yahya Ould | |
| dc.date | 2009-02-10 | |
| dc.date | 2009-02-19 | |
| dc.date.accessioned | 2026-07-07T12:43:24Z | |
| dc.date.available | 2026-07-07T12:43:24Z | |
| dc.description | Let $Γ=(V,E)$ be a reflexive relation having a transitive group of automorphisms and let $v\in V.$ Let $F$ be a subset of $V$ with $F\cap Γ^-(v)=\{v\}$. (i) If $F$ is finite, then $| Γ(F)\setminus F|\ge |Γ(v)|-1.$ (ii) If $F$ is cofinite, then $| Γ(F)\setminus F|\ge |Γ^- (v)|-1.$ In particular, let $G$ be group, $B$ be a finite subset of $G$ and let $F$ be a finite or a cofinite subset of $G$ such that $F\cap B^{-1}=\{1\}$. Then $| (FB)\setminus F|\ge |B|-1.$ The last result (for $F$ finite), is famous Moser-Scherck-Kemperman-Wehn Theorem. Its extension to cofinite subsets seems new. We give also few applications. | |
| dc.identifier | https://arxiv.org/abs/0902.1680 | |
| dc.identifier | http://arxiv.org/abs/0902.1680 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220406 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05E15; 11B13; 11B60, 11B34; 20K01; 20D60 | |
| dc.title | Extensions of the Moser-Scherck-Kemperman-Wehn Theorem | |
| dc.type | text |