39 citations · 72 across the 24 of their papers we have counts for
Showing 2009 · math.NTShow all
3 papers · 2 filters
math.NT2009
On the possible orders of a basis for a finite cyclic group
Peter Hegarty
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, fo…
math.NT2009
Independent sets in almost-regular graphs and the Cameron-Erdos problem for non-invariant linear equations
Peter Hegarty
We propose a generalisation of the Cameron-Erdos conjecture for sum-free sets to arbitrary non-translation invariant linear equations over Z in three or more variables and, using w…
math.NT2009
Answers to two questions posed by Farhi concerning additive bases
Peter Hegarty
Let A be an asymptotic basis for N and X a finite subset of A such that A\X is still an asymptotic basis. Farhi recently proved a new batch of upper bounds for the order of A\X in…