CPL - Chalmers Publication Library

# Permutations avoiding arithmetic patterns

Peter Hegarty (Institutionen för matematik)
Electron. J. Combin. Vol. 11 (2004), 1, p. 21 pages.

A permutation $\pi$ of an abelian group $G$ (that is, a bijection from $G$ to itself) will be said to avoid arithmetic progressions if there does not exist any triple $(a,b,c)$ of elements of $G$, not all equal, such that $c-b=b-a$ and $\pi(c)-\pi(b)=\pi(b)-\pi(a)$. The basic question is, which abelian groups possess such a permutation ? This and problems of a similar nature will be considered.