Tilings

By Federico Ardila, Richard P. Stanley. 2005

167 citations recorded by the source corpus.

A survey of tilings in the plane for a general audience.

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A Characterization of the Entropies of Multidimensional Shifts of Finite Type (2007, methodology): “Instead we rely on a theorem of Mozes [20] about the realization of substitution systems by SFTs.”
Entropies realizable by block gluing ℤd shifts of finite type (2015, methodology): “Rather than using the more general construction of Mozes (introduced in [17]) as was done in [9], we use the Robinson tilings from [21].”
Medvedev degrees of two-dimensional subshifts of finite type (2012, methodology): “Mozes [21, 22] and recently Hochman and Meyerovitch [14] have used the tiling methods of Wang [43] and Robinson [26] to construct two-dimensional subshifts of finite type with interesting dynamical properties.”
Continuous orbit equivalence rigidity (2015, methodology): “Building on the work of Schmidt on cocycle rigidity [25, 26], we obtain more examples of continuous orbit equivalence rigid systems, namely: • chessboards: the subshift consisting of all x ∈ {1, .”
Simple groups of dynamical origin (2015, background): “Groupoids and inverse semigroups are appropriate tools for the study of symmetries of quasiperiodic structures; see [2, 11, 12].”
Beta-expansions, natural extensions and multiple tilings associated with Pisot units (2009, unknown): “[ABEI01]), discrete geometry (Ito and Rao [IR06]) and automata ([Sie04]).”