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Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper, Barak Weiss (2012)

Annales de l’institut Fourier

We study infinite translation surfaces which are $ℤ$ -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Generalized triangular grids in digital geometry.

Nagy, Benedek (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Generalized Vitali systems of uniform type

Leif Mejlbro (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Generalized Whitney partitions

Michał Rams (2000)

Fundamenta Mathematicae

We prove that the upper Minkowski dimension of a compact set Λ is equal to the convergence exponent of any packing of the complement of Λ with polyhedra of size not smaller than a constant multiple of their distance from Λ.

Generation of optimal packings from optimal packings.

Gensane, Thierry (2009)

The Electronic Journal of Combinatorics [electronic only]

Geometric and combinatorial structure of a class of spherical folding tessellations – I

Catarina P. Avelino, Altino F. Santos (2017)

Czechoslovak Mathematical Journal

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

We investigate in a geometrical way the point sets of $ℝ$ obtained by the $β$ -numeration that are the $β$ -integers $ℤ_{β} \subset ℤ [β]$ where $β$ is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the $β$ -numeration, allowing to lift up the $β$ -integers to some points of the lattice $ℤ^{m}$ ( $m =$ degree of $β$ ) lying about the dominant eigenspace of the companion matrix of $β$ . When $β$ is in particular a Pisot number, this framework gives another proof of the fact that $ℤ_{β}$ is...