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Embedding tiling spaces in surfaces

Charles Holton, Brian F. Martensen (2008)

Fundamenta Mathematicae

We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...

Empilements de cercles et modules combinatoires

Peter HaÏssinsky (2009)

Annales de l’institut Fourier

Le but de cette note est de tenter d’expliquer les liens étroits qui unissent la théorie des empilements de cercles et des modules combinatoires et de comparer les approches à la conjecture de J.W. Cannon qui en découlent.

Equivalence classes of Latin squares and nets in P 2

Corey Dunn, Matthew Miller, Max Wakefield, Sebastian Zwicknagl (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The fundamental combinatorial structure of a net in P 2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in P 2 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in P 2 are empty to show some non-existence results for 4-nets in P 2 .

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