Related papers: The three-point function of general planar maps
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions,…
In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…
A formula is derived that provides generating functions for any multi-j-symbol, such as the 3-j-symbol, the 6-j-symbol, the 9-j-symbol, etc. The result is completely determined by geometrical objects (loops and curves) in the graph of the…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We obtain a very simple formula for the generating function of bipartite (resp. quasi-bipartite) planar maps with boundaries (holes) of prescribed lengths, which generalizes certain expressions obtained by Eynard in a book to appear. The…
In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for…
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…
The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have…
A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points…
We address the enumeration of q-coloured planar maps counted bythe number of edges and the number of monochromatic edges. We prove that the associated generating function is differentially algebraic,that is, satisfies a non-trivial…
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…
It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi,…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
We enumerate rooted 2-connected and 3-connected surface maps with respect to vertices and edges. We also derive the bivariate version of the large face-width result for random 3-connected maps. These results are then used to derive…
We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations…
The number of distinct maps (pre-maps) with a single vertex and valence $d$ is computed for any value of $d$. The types of maps (pre-maps) that we consider depend on whether the underlaying graph (pre-graph) is signed or unsigned and…