Model
Digital Document
Publisher
Florida Atlantic University
Description
The topic of this paper is tiling the integers with triples, or more precisely to write
Z as a disjoint union of translates of a given set of 3-subsets composed of basic shapes
called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define
an algorithm which returns a sequence of translates of P when given an initial subset
of Z representing integers that are already tiled. This algorithm is then adapted to
describe all possible tilings with triples from P using the action of certain signed
permutation matrices on a subset of za+b , uamdy the 2" Yectors with all entries ±1.
Given b > 2a, we research properties of the digraph of all possible tiling states and
some related digraphs.
Z as a disjoint union of translates of a given set of 3-subsets composed of basic shapes
called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define
an algorithm which returns a sequence of translates of P when given an initial subset
of Z representing integers that are already tiled. This algorithm is then adapted to
describe all possible tilings with triples from P using the action of certain signed
permutation matrices on a subset of za+b , uamdy the 2" Yectors with all entries ±1.
Given b > 2a, we research properties of the digraph of all possible tiling states and
some related digraphs.
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