Related papers: Partitions of $n$-valued maps

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to…

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the…

Let $X$ be a smooth projective variety. Define a stable map $f:C\to X$ to be "eventually smoothable" if there is an embedding $X\hookrightarrow\mathbb{P}^N$ such that $(C,f)$ occurs as the limit of a $1$-parameter family of stable maps to…

We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of a class of decompositions by must-join…

We present a multi-level graph partitioning algorithm based on the extreme idea to contract only a single edge on each level of the hierarchy. This obviates the need for a matching algorithm and promises very good partitioning quality since…

The partitions of the integers can be expressed exactly in an iterative and closed-form expression. This equation is derived from distributing the partitions of a number in a network that locates each partition in a unique and orderly…

Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any $n\neq 7$. The basis for this is an inequality for the partition function which…

The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…

A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.

In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known `strongly connected components' as well as another type of components we call `connected acyclic…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with…

A directed graph G (V, E) is strongly connected if and only if, for a pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is…

A Lambda (Card Lambda > aleph)-product space of {0,1} has a partition {X1,...,Xn} for any n a decomposition space of each Xi of which is self-similar.(February 16, 2015)

An affine vector space partition of $\operatorname{AG}(n,q)$ is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for…

The successive works of Terao as well as Stanley revealed that, for graphical arrangements, supersolvability and the existence of nice partitions are equivalent properties, both characterized by chordal graphs. In this paper, we further…

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…