Related papers: Noncommutative partial convexity via $\Gamma$-conv…

The notion of the quantum automorphism group of a graph was introduced by J. Bichon in 2003 and T. Banica in 2005 respectively. This article explores primarily the quantum automorphism group of a graph $\Gamma$, denoted by…

A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of…

We study closed smooth convex plane curves $\Gamma$ enjoying the following property: a pair of points $x,y$ can traverse $\Gamma$ so that the distances between $x$ and $y$ along the curve and in the ambient plane do not change; such curves…

It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to…

Let $\Gamma$ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in $\Gamma$ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of…

This note aims to study the iteration theory of noncommutative self-maps of bounded matrix convex domains. We prove a version of the Denjoy-Wolff theorem for the row ball and the maximal quantization of the unit ball of $\mathbb{C}^d$. For…

The non--commuting graph $\Gamma(G)$ of a non--abelian group $G$ is defined as follows. The vertex set $V(\Gamma(G))$ of $\Gamma(G)$ is $G\setminus Z(G)$ where $Z(G)$ denotes the center of $G$ and two vertices $x$ and $y$ are adjacent if…

For a connected graph $\Gamma=(V,E)$, a subset $R$ of ordered vertices in $V$ is said to be a resolving set in $\Gamma$, if the vector of distances to the vertices in $R$ is unique for each $u^{i}\in V(\Gamma)$. The metric dimension of…

We show that, if $\Gamma$ is a point group of $\mathbb{R}^{k+1}$ of order two for some $k\geq 2$ and $\mathcal S$ is a $k$-pseudomanifold which has a free automorphism of order two, then either $\mathcal S$ has a $\Gamma$-symmetric…

We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk…

In this article, we generalise a result of Pottmeyer from the multiplicative group of the algebraic numbers to almost split semiabelian varieties defined over number fields. This concerns a consequence of R\'emond's generalisation of…

The cyclic graph $\Gamma(S)$ of a semigroup $S$ is the simple graph whose vertex set is $S$ and two vertices $x, y$ are adjacent if the subsemigroup generated by $x$ and $y$ is monogenic. In this paper, we classify the semigroup $S$ such…

Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…

Let $G$ be 2-generated group. The generating graph $\Gamma(G)$ of $G$ is the graph whose vertices are the elements of $G$ and where two vertices $g$ and $h$ are adjacent if $G = \langle g, h \rangle.$ This definition can be extended to a…

We study large linear structures inside sets arising in the theory of norm-attaining operators. We provide several results in the context of lineability, spaceability, maximal-spaceability, and $(\alpha, \beta)$-spaceability for sets of…

We generalize the main result of math.RA/9608214 concerning the convex embeddings of a chain Gamma in a lexicographic power Delta^Gamma. For a fixed nonempty chain Delta, we derive necessary and sufficient conditions for the existence of…

We investigate the $\Gamma$-convergence of Ambrosio-Tortorelli type-functionals for circle valued functions, in the case of volume terms with linear growth. We show the emergence of a non-local $\Gamma$-limit, which is due to the…

We consider sets and maps defined over an o-minimal structure over the reals, such as real semi-algebraic or subanalytic sets. A {\em monotone map} is a multi-dimensional generalization of a usual univariate monotone function, while the…

In a number of recent works [6, 7] the authors have introduced and studied a functor $\mathcal{F}_k$ which associates to each loose graph $\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a…

It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial…