Additive and multiplicative properties of point sets based on beta-integers.

DOI10.1016/S0304-3975(02)00503-0zbMath1036.11034OpenAlexW2129447422MaRDI QIDQ1401383

Rudolf Krejcar, Christiane Frougny, Jean-Pierre Gazeau

Publication date: 17 August 2003

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-3975(02)00503-0

zbMATH Keywords

tilingMeyer setsinflation rules\(\beta\)-expansionsbeta-integerquadratic PV numberQuasicrystal

Mathematics Subject Classification ID

Combinatorics on words (68R15) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Automata sequences (11B85) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items

Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number ⋮ On gaps in Rényi \(\beta\)-expansions of unity for \(\beta>1\) an algebraic number ⋮ Complexity of infinite words associated with beta-expansions ⋮ Symmetry groups for beta-lattices ⋮ Beta-shifts, their languages, and computability ⋮ Abelian complexity of infinite words associated with quadratic Parry numbers ⋮ Tilings for Pisot beta numeration ⋮ Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers ⋮ Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words ⋮ Repetitions in beta-integers ⋮ Asymptotic behavior of beta-integers ⋮ Arithmetic Meyer sets and finite automata ⋮ A classification of (some) Pisot-cyclotomic numbers

Cites Work

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