相关论文: Subspaces intersecting each element of a regulus i…

Let $\mathrm{PG}(n-1,q)$ denote the $(n-1)$-dimensional projective space over $\mathbb{F}_q$. We investigate the intersection of two Desarguesian $(h-1)$-spreads of $\mathrm{PG}(kh-1,q)$ and show that it is determined by a subgeometry over…

A {\em pseudo-arc} in $\mathrm{PG}(3n-1,q)$ is a set of $(n-1)$-spaces such that any three of them span the whole space. A pseudo-arc of size $q^n+1$ is a {\em pseudo-oval}. If a pseudo-oval $\mathcal{O}$ is obtained by applying field…

We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume…

We study in-depth those rings $R$ for which, there exists a fixed $n\geq 1$, such that $u^n-1$ lies in the subring $\Delta(R)$ of $R$ for every unit $u\in R$. We succeeded to describe for any $n\geq 1$ all reduced $\pi$-regular…

We provide a characterisation of $(n-1)$-spreads in $\mathrm{PG}(rn-1,q)$ that have $r$ normal elements in general position. In the same way, we obtain a geometric characterisation of Desarguesian $(n-1)$-spreads in $\mathrm{PG}(rn-1,q)$,…

Clubs of rank k are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arcs known as KM-arcs, they renewed their interest. This paper aims to study clubs of…

In this paper, we investigate the Andr\'e/Bruck-Bose representation of certain $\mathbb{F}_q$-linear sets contained in a line of $\text{PG}(2,q^t)$. We show that scattered $\mathbb{F}_q$-linear sets of rank $3$ in $\text{PG}(1,q^3)$…

We introduce the notion of halfspaces associated to a group splitting, and investigate the relationship between the coarse geometry of the halfspaces and the coarse geometry of the group. Roughly speaking, the halfspaces of a group…

Let K be a field admitting a cyclic Galois extension of degree n. The main result of this paper is a decomposition theorem for the space of alternating bilinear forms defined on a vector space of odd dimension n over K. We show that this…

In: S.G. Barwick and W.A. Jackson. Sublines and subplanes of PG(2,q^3) in the Bruck--Bose representation in PG(6,q). Finite Fields Th. App. 18 (2012) 93--107., the authors determine the representation of order-q-subplanes and…

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also…

This paper studies {\em strong blocking sets} in the $N$-dimensional finite projective space $\mathrm{PG}(N,q)$. We first show that certain unions of blocking sets cannot form strong blocking sets, which leads to a new lower bound on the…

A special case of a combinatorial theorem of De Bruijn and Erdos asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this assertion in…

We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…

We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…

We consider the Andr\'e/Bruck-Bose representation of the projective plane $\mathrm{PG}(2,q^n)$ in $\mathrm{PG}(2n,q)$. We investigate the representation of $\mathbb{F}_{q^k}$-sublines and $\mathbb{F}_{q^k}$-subplanes of…

The goal of this note is to create a sound framework for the interplay between field reduction for finite projective spaces, the general semilinear groups acting on the defining vector spaces and the projective semilinear groups. This…

In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively.…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…