Related papers: Sequences in Overpartitions
This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
In this short article, we consider a problem about $2$-partition of the vertices of a graph. If a graph admits such a partition into some 'small' graphs, then the number of edges cross an arbitrary cut of the graph $e(S,S^{c})$ has a nice…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…
Deep networks have shown impressive performance in the image restoration tasks, such as image colorization. However, we find that previous approaches rely on the digital representation from single color model with a specific mapping…
Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.
Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and…
Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are…
We apply matrix theory over $\mathbb{F}_2$ to understand the nature of so-called "successful pressing sequences" of black-and-white vertex-colored graphs. These sequences arise in computational phylogenetics, where, by a celebrated result…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
The attempts to prove the Four Color Problem last for long years. A little hope arises that the properties of the minimal partial triangulations will be very useful for the solution of the Four Color Problem. That is why the material of…
A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
This paper serves as the first extension of the topic of dominator colorings of graphs to the setting of digraphs. We establish the dominator chromatic number over all possible orientations of paths and cycles. In this endeavor we discover…
We study vertex colourings of digraphs so that no out-neighbourhood is monochromatic and call such a colouring an {\bf out-colouring}. The problem of deciding whether a given digraph has an out-colouring with only two colours (called a…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
A revised formula for the inclusive cross section for double parton scattering in terms of the modified collinear two-parton distributions extracted from deep inelastic scattering is suggested. The possible phenomenological issues are…
Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze several characteristics of simple drawings of complete…
The paper deals with real valued sequences and its distribution on real line.
We consider the features of multiparticle tree cross sections in scalar theories in the framework of a semiclassical approach. These cross sections at large multiplicities have exponential form, and the properties of the exponent in…