Combinatorial properties in cut-and-project sets: order beyond periodicity

Christoph Richard, Fau Erlangen-Nürnberg
2015 unpublished
1 / 30 order beyond periodicity motivation motivation every lattice Λ ⊂ R d is uniformly discrete: ∃r > 0 ∀x ∈ R d : |Λ ∩ B r (x)| ≤ 1 relatively dense: ∃R > 0: ΛB R (0) = R d periodic with d linearly independent periods "pure point diffractive" we are interested in "ordered" point sets which generalise lattices I: order beyond periodicity II: cut-and-project sets: geometry and combinatorics III: cut-and-project sets: diffraction and harmonic analysis 2 / 30 order beyond periodicity motivation