Shalom Eliahou

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Let D n be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size µ D n (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of D n of cardinality r and s respectively. It is shown by construction that µ D n (r, s) is bounded above by the known(More)
The Cauchy-Davenport theorem states that, if p is prime and A, B are nonempty subsets of cardinality r, s in Z/pZ, the cardinality of the sumset A + B = {a + b | a ∈ A, b ∈ B} is bounded below by min(r + s − 1, p); moreover, this lower bound is sharp. Natural extensions of this result consist in determining, for each group G and positive integers r, s ≤(More)