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Let $\sum$ be a flat surface of genus $g$ with cone type singularities. Given a bipartite graph $Γ$ isoradially embedded in $\sum$ , we define discrete analogs of the $2^{2 g}$ Dirac operators on $\sum$ . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair $Γ \subset \sum$ for these discrete Dirac operators to be Kasteleyn matrices of the graph $Γ$ . As a consequence, if these conditions are met, the partition function of the dimer...

Discrete geometry and numeration

Valérie Berthé (2009)

Actes des rencontres du CIRM

Discrete isothermic surfaces.

Ulrich Pinkall, Alexander Bobenko (1996)

Journal für die reine und angewandte Mathematik

Disks with Special Properties of Densest Packings.

P. Schmitt (1991)

Discrete & computational geometry

Dissections into equilateral triangles.

Zsolt Tuza (1991)

Elemente der Mathematik

Dissections of Regular Polygons into Triangles of Equal Areas.

E.A. Kasimatis (1989)

Discrete & computational geometry

Distributing points on the sphere. I.

Kantanforoush, Ali, Shahshahani, Mehrdad (2003)

Experimental Mathematics

Distribution of lattice points on hyperbolic surfaces

Vsevolod F. Lev (1996)

Acta Arithmetica

Let two lattices $Λ^{'}, Λ^{''} \subset ℝ^{s}$ have the same number of points on each hyperbolic surface $| x ₁ . . . x_{s} | = C$ . We investigate the case when Λ’, Λ” are sublattices of $ℤ^{s}$ of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.

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Dihedral f-tilings of the sphere by equilateral and scalene triangles. III.

Dihedral f-tilings of the sphere by equilateral and scalene triangles-I

Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles.

Discrete convexity.

Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

Discrete geometry and numeration

Discrete isothermic surfaces.

Disks with Special Properties of Densest Packings.

Dissections into equilateral triangles.

Dissections of Regular Polygons into Triangles of Equal Areas.

Distributing points on the sphere. I.

Distribution of lattice points on hyperbolic surfaces

Divisible tilings in the hyperbolic plane.

Domino tilings and products of Fibonacci and Pell numbers.

Double-Lattice Packings of Convex Bodies in the Plane.

Dreieckszerlegungen

Dynamics of icosahedral viruses: what does viral tiling theory teach us?

Currently displaying 21 – 37 of 37