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Determining pure discrete spectrum for some self-affine tilings

Abstract : By the algorithm implemented in the paper by Akiyama-Lee [Adv. Math. 226(4):2855 13;2883, 2011] and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to 2, and some cases of planar tilings generated by boundary substitutions due to Kenyon [Geom. Func. Anal. 6:471 13;488, 1996].
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Shigeki Akiyama, Franz Gähler, Jeong-Yup Lee. Determining pure discrete spectrum for some self-affine tilings. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.305--316. ⟨hal-01188903⟩

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