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We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.
In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related…
We consider the Hurwitz action on quasipositive factorizations of a 3-braid. In a previous paper, for any given 3-braid we described a certain finite set which contains at least one representative of each orbit. Here we give an algorithm to…
We study the asymptotic behaviour of random factorizations of the $n$-cycle into transpositions of fixed genus $g>0$. They have a geometric interpretation as branched covers of the sphere and their enumeration as Hurwitz numbers was…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partially ordered sets can be studied under simultaneous partially…
The Temperley--Lieb algebra is a finite dimensional associative algebra that arose in the context of statistical mechanics and occurs naturally as a quotient of the Hecke algebra arising from a Coxeter group of type $A$. It is often…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…
The set of factorizations of permutations in to $m$ transpositions of some symmetric group $\mathcal{S}_n$ is naturally in bijection with the set of graphs of order $n$ and size $m$ with both edges and vertices labeled. We define a notion…
The higher connectivity at infinity for mapping class groups of surfaces with boundary components and punctures is understood with the exceptions of the mapping class groups for the closed surfaces of genus 3 and 4. In this paper we prove a…
This article is a continuation of my former article "On Connectivity Spaces". After some brief historical references relating to the subject, separation spaces and then adjoint notions of connective representation and connective foliation…
The proper parts of face lattices of convex polytopes are shown to satisfy a strong form of the Cohen--Macaulay property, namely that removing from their Hasse diagram all edges in any closed interval results in a Cohen--Macaulay poset of…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive…
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…