We study tilings of groups with mutually disjoint difference sets. Some necessary existence conditions are proved and shown not to be sufficient. In the case of tilings with two difference sets we show the equivalence to skew Hadamard difference sets, and prove that they must be normalized if the group is abelian. Furthermore, we present some constructions of tilings based on cyclotomy and investigate tilings consisting of Singer difference sets.
@article{10_37236_5157,
author = {Ante \'Custi\'c and Vedran Kr\v{c}adinac and Yue Zhou},
title = {Tiling groups with difference sets},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/5157},
zbl = {1327.05039},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5157/}
}
TY - JOUR
AU - Ante Ćustić
AU - Vedran Krčadinac
AU - Yue Zhou
TI - Tiling groups with difference sets
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5157/
DO - 10.37236/5157
ID - 10_37236_5157
ER -
%0 Journal Article
%A Ante Ćustić
%A Vedran Krčadinac
%A Yue Zhou
%T Tiling groups with difference sets
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5157/
%R 10.37236/5157
%F 10_37236_5157
Ante Ćustić; Vedran Krčadinac; Yue Zhou. Tiling groups with difference sets. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/5157
