Göteborgs universitets publikationer

# Permutations destroying arithmetic progressions in finite cyclic groups

Författare och institution:
Peter Hegarty (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Anders Martinsson (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
The Electronic Journal of Combinatorics, 22 ( 4 ) s. Art. no. P4.39
ISSN:
1077-8926
Antal sidor:
11
Publikationstyp:
Publiceringsår:
2015
Språk:
engelska
Fulltextlänk:
Fulltextlänk (lokalt arkiv):
Sammanfattning (abstract):
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).
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Diskret matematik
Nyckelord:
Permutation, arithmetic progression, finite cyclic group
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
218523