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Scientific article
English

Sumsets in dihedral groups

Published inEuropean journal of combinatorics, vol. 27, no. 4, p. 617-628
Publication date2006
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.

Citation (ISO format)
ELIAHOU, Shalom, KERVAIRE, Michel. Sumsets in dihedral groups. In: European journal of combinatorics, 2006, vol. 27, n° 4, p. 617–628. doi: 10.1016/j.ejc.2003.09.023
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ISSN of the journal0195-6698
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