Related papers: Combinatorics of positional colored compositions

We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…

Given a graph G (or more generally a matroid embedded in a projective space), we construct a sequence of varieties whose geometry encodes combinatorial information about G. For example, the chromatic polynomial of G (giving at each m>0 the…

This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…

Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated Lie algebra are proposed. It is shown that in the second…

Suppose that $nk$ points in general position in the plane are colored red and blue, with at least $n$ points of each color. We show that then there exist $n$ pairwise disjoint convex sets, each of them containing $k$ of the points, and each…

We consider the cross-modal task of producing color representations for text phrases. Motivated by the fact that a significant fraction of user queries on an image search engine follow an (attribute, object) structure, we propose a…

We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound…

In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques, we determine the expected number of blocks when the vertices…

Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…

We establish closed-form expansions for the number of colorings of a path or cycle on n vertices with colors from 1,...,x such that adjacent vertices are colored differently or with colors from y+1,...x.

We define a $P$-compelling coloring as a proper coloring of the vertices of a graph such that every subset consisting of one vertex of each color has property $P$. The $P$-compelling chromatic number is the minimum number of colors in such…

We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.

A topological space is introduced in this paper. Just liking the plane, it's continuous, however its $n+1$ regions couldn't be mutually adjacent. Some important phenomenon about its cross-section are discussed. The geometric generating…

In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…

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…

We consider sequences counting integer partitions in two colors (red and blue) in which the even parts occur only in blue color. We focus on subsequences defined by constraints on the parity and color of the summands. We establish formulas…

This paper is intended to provide concrete examples of concepts discussed elsewhere in this volume, especially splittings of groups and non-positively curved cube complexes but also other things. The idea of the construction (configuration…

We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…

This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…

Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…