Related papers: An algorithm for map enumeration

Based on Hopf algebra of rooted trees introduced by Connes and Kreimer, we construct a class of linear maps on noncommutative polynomial algebra in two indeterminates, namely rooted tree maps. We also prove that their maps induce a class of…

We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with…

We prove that the mirror map is the SYZ map for every toric Calabi-Yau surface. As a consequence one obtains an enumerative meaning of the mirror map. This involves computing genus-zero open Gromov-Witten invariants, which is done by…

Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this…

The enumeration of linear $\lambda$-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. Zeilberger and Giorgetti (2015) gave a recursive bijection between planar linear normal $\lambda$-terms…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

Our work studies the enumeration and random generation of unlabeled combinatorial classes of unrooted graphs. While the technique of vertex pointing provides a straightforward procedure for analyzing a labeled class of unrooted graphs by…

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 consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…

We give explicit formulas enumerating 4-regular labelled and unlabelled one-face maps.

A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…

In 1997, Schaeffer described a bijection between Eulerian planar maps and some trees. In this work we generalize his work to a bijection between bicolorable maps on a surface of any fixed genus and some unicellular maps with the same genus.…

The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…

Hartsfield and Ringel constructed orientable quadrangular embeddings of the complete graph $K_n$ for $n\equiv 5 \pmod 8$, and nonorientable ones for $n \ge 9$ and $n\equiv 1 \pmod 4$. These provide minimal quadrangulations of their…

We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams…

We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…

We give new upper bounds for the number of nonconstant holomorphic maps depending only on the genus. Our estimates improve previously known bounds. The proof is based on the study of pullbacks of holomorphic differentials, together with…

There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…

Let G be a compact Lie group or a complex reductive affine algebraic group. We explore induced mappings between G-character varieties of surface groups by mappings between corresponding surfaces. It is shown that these mappings are…

We construct an explicit bijection between bipartite pointed maps of an arbitrary surface $\mathbb{S}$, and specific unicellular blossoming maps of the same surface. Our bijection gives access to the degrees of all the faces, and distances…