Related papers: Planar maps and continued fractions

We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all surfaces, that is orientable and non-orientable as well. This…

This paper is a sequel of arXiv:2109.06394. In this paper, we consider a kind of inverse problem of multipliers. The problem is to count number of isospectral correspondences, correspondences which has the same combination of multipliers.…

We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…

This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…

This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…

By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing…

Given a plane graph $G$ (i.e., a planar graph with a fixed planar embedding) and a simple cycle $C$ in $G$ whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we…

We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary. As a consequence, we count the number of…

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…

We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…

We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges form a planar graph. By planar duality this is equivalent to packing cuts…

We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also…

New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate…

In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate…

In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…

We present two graph drawing algorithms based on the recently defined "grand-Schnyder woods", which are a far-reaching generalization of the classical Schnyder woods. The first is a straight-line drawing algorithm for plane graphs with…

We introduce and study the notion of a locally proper map between topological spaces. We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from…

In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…