Extensions of the Scherk-Kemperman Theorem
نویسنده
چکیده
Let Γ = (V,E) be a reflexive relation with a transitive automorphisms group. Let v ∈ V and let F be a finite subset of V with v ∈ F. We prove that the size of Γ(F ) (the image of F ) is at least |F |+ |Γ(v)| − |Γ−(v) ∩ F |. Let A,B be finite subsets of a group G. Applied to Cayley graphs, our result reduces to following extension of the Scherk-Kemperman Theorem, proved by Kemperman: |AB| ≥ |A|+ |B| − |A ∩ (cB)|, for every c ∈ AB.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 117 شماره
صفحات -
تاریخ انتشار 2010