39 citations · 72 across the 24 of their papers we have counts for
12 papers · 1 filter
Permutations destroying arithmetic progressions in finite cyclic groups
Peter Hegarty, Anders Martinsson
A permutation πof an abelian group G is said to destroy arithmetic progressions (APs) if, whenever (a,b,c) is a non-trivial 3-term AP in G, that is c-b=b-a and a,b,c are not all eq…
Why should one expect to find long runs of (non)-Ramanujan primes ?
Peter Hegarty
Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all primes are RPs asymptotically, one obtains runs of consecutives RPs (resp. non-RPs…
On m-covering families of Beatty sequences with irrational moduli
Peter Hegarty
We generalise Uspensky's theorem characterising eventual exact (e.e.) covers of the positive integers by homogeneous Beatty sequences, to e.e. m-covers, for any m \in \N, by homoge…
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…
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…
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…