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Tilings associated with non-Pisot matrices

Maki FurukadoShunji ItoE. Arthur Robinson — 2006

Annales de l’institut Fourier

Suppose A G l d ( ) has a 2-dimensional expanding subspace E u , satisfies a regularity condition, called “good star”, and has A * 0 , where A * is an of A . A morphism θ of the free group on { 1 , 2 , , d } is called a of A if it has structure matrix A . We show that there is a Θ whose “boundary substitution” θ = Θ is a non-abelianization of A . Such a tiling substitution Θ leads to a self-affine tiling of E u 2 with A u : = A | E u G L 2 ( ) as its expansion. In the last section we find conditions on A so that A * has no negative entries.

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