Research
Papers
Published
A class of aperiodic honeycombs with tuneable mechanical properties, R. Moat, D. Clarke, F. Carter, D. Rust, I. Jowers
Applied Materials Today 37, 102127 (2024) - DOI (open access online)
Automorphism groups of random substitution subshifts, R. Fokkink, D. Rust, V. Salo
Indagationes Mathematicae (2023) in print - arXiv
Spectral properties of substitutions on compact alphabets, N. Mañibo, D. Rust, J. Walton
Bulletin of the London Mathematical Society 55, 2425 - 2445 (2023) - arXiv, DOI (open access online)
Measure theoretic entropy of random substitution subshifts, P. Gohlke, A. Mitchell, D. Rust, T. Samuel
Annales Henri Poincaré, 24, 277 - 323 (2023) - arXiv, DOI (open access online)
Topological mixing of random substitutions, E. D. P. Miro, D. Rust, L. Sadun, G. S. Tadeo
Israel Journal of Mathematics, 255, 123 - 153 (2022) - arXiv, DOI
Queen reflections: A modification of Wythoff's Nim, R. Fokkink, D. Rust
International Journal of Game Theory (2022) in print - arXiv, DOI (open access online)
Zeckendorf representations and mixing properties of sequences, N. Manibo, E. D. P. Miro, D. Rust, G. S. Tadeo
Tsukuba Journal of Mathematics, 44(2), 251 - 269 (2020) - arXiv, DOI
Periodic points in random substitution subshifts, D. Rust
Monatshefte für Mathematik, 193, 683 - 704 (2020) - arXiv, DOI
Shifts of finite type and random substitutions, P. Gohlke, D. Rust, T. Spindeler
Discrete and Continuous Dynamical Systems, 39(9), 5085 - 5103 (2019) - arXiv, DOI
Dynamical systems arising from random substitutions, D. Rust, T. Spindeler
Indagationes Mathematicae, 29(4), 1131 - 1155 (2018) - arXiv, DOI
Beyond primitivity for one-dimensional substitution subshifts and tiling spaces, G. R. Maloney, D. Rust
Ergodic Theory and Dynamical Systems, 38(3), 1086 - 1117 (2018) - arXiv, DOI
Computations for symbolic substitutions, S. Balchin, D. Rust
Journal of Integer Sequences, 20, Article 17.4.1 (2017) - arXiv, DOI (open access online)
An uncountable set of tiling spaces with distinct cohomology, D. Rust
Topology and its Applications, 205, 58 - 81 (2016) - arXiv, DOI
Book Chapters
Corner the Empress, R. Fokkink, G. F. Ortega, D. Rust
Games of No Chance 6 (2023) in print - arXiv
Thesis
Cohomology of Tiling Spaces: Beyond Primitive Substitutions, D. Rust
PhD Thesis, University of Leicester, Leicester, (2016) Leicester research archive
Images generated in Mathematica by Tony Samuel, in collaboration with Andrew Mitchell.
Programs
Grout
Authors: S. Balchin, D. Rust
Grout is a free user-friendly program for Windows and Mac which can calculate various topological and combinatorial properties of primitive symbolic substitutions.
For an explanation of the computations that Grout performs, we have provided documentation on the arXiv.
You can download Grout from Github.
Slides
Substitutions on compact alphabets - talk given in the Ben-Gurion Probability and Ergodic Theory Seminar (13/01/22)
Random substitutions - (Youtube video) - talk given in the One World Combinatorics on Words Seminar (8/11/21)
Substitution subshifts on compact alphabets - talk given in the Vienna Ergodic Theory Seminar (8/04/21)
Random substitutions and their dynamical invariants - talk given at CIRM workshop (talk starts at bookmark position 31) - Algebraic and Combinatorial Invariants of Subshifts and Tilings (11/01/21)
Random substitutions and Rauzy fractals - talk given in various places in 2020 and 2021
Ordered cohomology and co-dimension one cut-and-project sets - talk given in the Jena Mathematics Colloquium (24/11/16)
The strange topology of aperiodic tiling spaces and their cohomology - talk given in the Leicester PhD Mathematics Seminar (2/12/15)