Some explicit constructions of ternary non-full-rank tilings of abelian groups
Abstract
A tiling of a finite abelian group G is a pair (A,B) of subsets of G, such that both A and B contain the identity element e of G and every g ∈ G can be uniquely written in the form g = ab, where a ∈ A and b ∈ B. A tiling (A,B) of G is called full-rank if hAi = hB >= G, Otherwise, it is called a non-full rank tiling. In this paper, we show some explicit constructions of non-full rank tilings of 3−groups of order 3^4.
Copyright © 2017 Khalid Amin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
K. Amin, Some explicit constructions of ternary non-full-rank tilings of abelian groups, J. Math. Comput. Sci. 7 (2017), 941–947.
BibTeX
@article{Amin2017,
author = {Amin, Khalid},
title = {Some explicit constructions of ternary non-full-rank tilings of abelian groups},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {941--947},
doi = {}
}