Related papers: Friezes from surfaces and Farey triangulation
Given a certain triangulation of a punctured surface with boundary, we construct a new triangulated surface without punctures which covers it. This new surface is naturally equipped with an action of a group of order two, and its quotient…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials:…
Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles…
We show that if a disc triangulation has all internal vertex degrees at least 6, then the full triangulation may be determined from the pairwise graph distance between boundary vertices. A similar result holds for quadrangulations with all…
We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.
Frieze patterns are defined by objects of a category of Dyck paths, to do that, it is introduced the notion of diamond of Dynkin type An. Such diamonds constitute a tool to build integral frieze patterns.
We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the process we define a new class of…
We prove that the infinite friezes arising from the tubes of a given cluster algebra of acyclic affine type all have the same growth coefficients. Our proof uses identities satisfied by theta functions. This generalizes previous results in…
Percolation of fine particles (fines) in a static bed of larger particles is central to many industrial and natural processes. Non-cohesive fines either pass through the bed or become trapped depending on multiple factors including particle…
For any integer $x$, let $T_x$ denote the triangular number $\frac{x(x+1)}{2}$. In this paper we give a complete characterization of all the triples of positive integers $(\alpha, \beta, \gamma)$ for which the ternary sums $\alpha x^2…
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this…
We prove three-dimensional Worsey-Farin refinements inherit their parent triangulations' shape-regularity.
A well-known result of Walsh states that if $\mathcal T^*$ is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components, then every properly embedded, two-sided, incompressible…
We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge-to-edge tilings of the sphere by congruent triangles.…
The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.
We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its $\partial\overline\partial$-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at…
A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…
The deformation theory of affine cones over polarized projective varieties, initiated by Pinkham and further developed by Schlessinger and Wahl, is central to the study of singularities and graded deformation functors. For a projective…
We introduce the notion of positive local combinatorial dividing-lines in model theory. We show these are equivalently characterized by indecomposable algebraically trivial Fraisse classes and by complete prime filter classes. We exhibit…