Permutations destroying arithmetic progressions in finite cyclic groups
Journal article, 2015

A permutation \pi of 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 equal, then (\pi(a),\pi(b),\pi(c)) is not an AP. In a paper from 2004, the first author conjectured that such a permutation exists of Z/nZ, for all n except 2,3,5 and 7. Here we prove, as a special case of a more general result, that such a permutation exists for all n >= n_0, for some explcitly constructed number n_0 \approx 1.4 x 10^{14}. We also construct such a permutation of Z/pZ for all primes p > 3 such that p = 3 (mod 8).

arithmetic progression

Permutation

finite cyclic group

Author

Peter Hegarty

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Anders Martinsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Electronic Journal of Combinatorics

1097-1440 (ISSN) 1077-8926 (eISSN)

Vol. 22 4 Art. no. P4.39-

Roots

Basic sciences

Subject Categories

Discrete Mathematics

More information

Created

10/7/2017