Related papers: Partitions of groups
Scrum is a structured framework to support complex product development. However, Scrum methodology faces a challenge of managing large teams. To address this challenge, in this paper we propose a solution called Scrum of Scrums. In Scrum of…
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u')…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially…
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that none of the parts can be written as the sum of smaller…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
The number of parts in the partitions (resp. distinct partitions) of $n$ with parts from a set were considered. Its generating functions were obtained. Consequently, we derive several recurrence identities for the following functions: the…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
We state and prove a theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of stationary population identity. Applications of this theorem for practical…
We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…
To partition a sequence of n integers into subsets with prescribed sums is an NP-hard problem in general. In this paper we present an efficient solution for the homogeneous version of this problem; i.e. where the elements in each subset add…
A method is given for calculation of a distribution of small particles, embedded in a medium, so that the resulting medium would have a desired radiation pattern for the plane wave scattering by this medium.
Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. We introduce a statistical framework for cross-sectional observations of groups with exclusive…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…