Related papers: Friezes from surfaces and Farey triangulation
We consider a stabilized finite element method for the Darcy problem on a surface based on the Masud-Hughes formulation. A special feature of the method is that the tangential condition of the velocity field is weakly enforced through the…
We prove that the quivers with potentials associated to triangulations of surfaces with marked points, and possibly empty boundary, are non-degenerate, provided the underlying surface with marked points is not a closed sphere with exactly 5…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.
We construct frieze patterns of type D_N with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram…
A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral…
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…
We introduce mutation along infinite admissible sequences for infinitely marked surfaces, that is surfaces with infinitely many marked points on the boundary. We show that mutation along such admissible sequences produces a preorder on the…
In this article, we construct SL$_k$-friezes using Pl\"ucker coordinates, making use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of $k$-spaces in $n$-space via the Pl\"ucker embedding. When this cluster…
This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump across the interface. In the method, the triangulation does not…
In this paper we use recollements to investigate partially wrapped Fukaya categories of surfaces with marked points. In particular, we show that cutting surfaces gives rise to recollements of the corresponding partially wrapped Fukaya…
We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable…
We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…
Motivated by cluster ensembles, we introduce a new variant of frieze patterns associated to acyclic cluster algebras, which we call ${\bf Y}\textit{-frieze patterns}$. Using the mutation rules for ${\bf Y}$-variables, we define a large…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a $T$-path formula expressing the Laurent…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
We use a class of Farey graphs introduced by the final three authors to enumerate the tame friezes over $\mathbb{Z}/n\mathbb{Z}$. Using the same strategy we enumerate the tame regular friezes over $\mathbb{Z}/n\mathbb{Z}$, thereby reproving…