Charles Radin, Lorenzo Sadun
An Algebraic Invariant for Substitution Tiling Systems
Preprint series: ESI preprints

MSC:

52C22 Tilings in $n$ dimensions, See also {05B45, 51M20}

52C20 Tilings in $2$ dimensions, See also {05B45, 51M20}

Abstract: We consider tilings of Euclidean spaces by polygons or polyhedra, in
particular, tilings made by a substitution process, such as the
Penrose tilings of the plane. We define an isomorphism invariant
related to a subgroup of rotations and compute it for various
examples. We also extend our analysis to more general dynamical
systems.
Keywords: tilings of Euclidean spaces, isomrophism invariant