Some explicit constructions of ternary non-full-rank tilings of abelian groups

Khalid Amin

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.

https://doi.org/10.28919/jmcs/3217


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How to Cite this Article:

Khalid Amin, Some explicit constructions of ternary non-full-rank tilings of abelian groups, Journal of Mathematical and Computational Science, Vol 7, No 5 (2017), 941-947

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.

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