On the possible orders of a basis for a finite cyclic group
Number Theory
2009-07-04 v2 Combinatorics
Abstract
We prove a conjecture of Dukes and Herke concerning the possible orders of a basis for the cyclic group Z_n, namely : For each k \in N there exists a constant c_k > 0 such that, for all n \in N, if A \subseteq Z_n is a basis of order greater than n/k, then the order of A is within c_k of n/l for some integer l \in [1,k]. The proof makes use of various results in additive number theory concerning the growth of sumsets.
Cite
@article{arxiv.0906.5484,
title = {On the possible orders of a basis for a finite cyclic group},
author = {Peter Hegarty},
journal= {arXiv preprint arXiv:0906.5484},
year = {2009}
}
Comments
5 pages, no figures. This is v2 : a typo in eq. (2.1) has been corrected