Related papers: Enumerative and bijective aspects of combinatorial…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
This paper summarizes our latest understanding and results about the application of the Mathematics Of Enumeration to Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Some preliminaries of permutation groups have…
Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…
One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of…
A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…