On the Pisot Substitution Conjecture

S Akiyama (1) , M Barge (2) , V Berthé (3) , J.-y Lee (4) , A Siegel (5)

1 Institute of Mathematics, University of Tsukuba
2 Department of Mathematical Sciences
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 Department of Animal Science and Biotechnology, College of Agriculture and Life Sciences
5 Dyliss - Dynamics, Logics and Inference for biological Systems and Sequences

This survey is concerned with the different existing formulations of the so-called Pisot conjecture : the authors start by stating the one-dimensional conjecture in various formalisms and then discuss the extension of this conjecture in higher dimensions.

Mots clés: Tiling space; substitution; Pisot number; discrete spectrum; cut-and-project scheme; beta-numeration; Delone set; Meyer set; model set; coincidence

Domaines: Bio-informatique [q-bio.QM]

S Akiyama, M Barge, V Berthé, J.-y Lee, A Siegel. On the Pisot Substitution Conjecture. Mathematics of Aperiodic Order, 309, Springer, pp.33-72, 2015, Progress in mathematics, 978-3-0348-0903-0. ⟨10.1007/978-3-0348-0903-0_2⟩. ⟨hal-01196318⟩