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Abstract: Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation a...
For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. In this paper, we...
We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process.
The Tutte polynomial G(X, Y ) of a graph G is a classical invariant,important in combinatorics and statistical mechanics. An important feature of the Tutte polynomial is the duality for planar graphs...
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi–Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface.
Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3–manifolds. We prove, by a construc...
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann’s ...
Counting Euclidean triangulations with vertices in a finite set C of the convex hull Conv(C ) of C is difficult in general, both algorithmically and theoretically. The aim of this paper is to describ...
It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangula...
Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" a...
We connect k-triangulations of a convex n-gon to the theory of Schubert polynomials. We use this connection to prove that the simplicial complex with k-triangulations as facets is a vertex-decomposabl...
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition.
Develin and Sturmfels showed that regular triangulations of n􀀀1  d􀀀1 can be thought as tropical polytopes. Tropical oriented matroids were de ned by Ardila and Develin, and were ...
Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesi...
We examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform triangulations. For ...

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