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Sumsets in dihedral groups

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Published in European Journal of Combinatorics. 2006, vol. 27, no. 4, p. 617 - 628
Abstract Let Dn 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 μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value of μG(r, s), where G is any abelian group of order 2n. We conjecture that this upper bound is sharp, and prove that it really is if n is a prime power.
Stable URL https://archive-ouverte.unige.ch/unige:12106
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Deposited on : 2010-10-15

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