相关论文: Sets of generators blocking all generators in fini…

Some classical polar spaces admit polar spaces of the same rank as embedded polar spaces (often arisen as the intersection of the polar space with a non-tangent hyperplane). In this article we look at sets of generators that behave…

Cameron-Liebler sets were originally defined as collections of lines (`line classes') in $\mathrm{PG}(3,q)$ sharing certain properties with line classes of symmetric tactical decompositions. While there are many equivalent…

In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets…

There are 6 families of finite polar spaces of rank $3$. The set of lines in a rank $3$ polar space form a rank $5$ association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some…

A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite…

Let $n$ be a positive integer. Denote by $\mathrm{PG}(n,q)$ the $n$-dimensional projective space over the finite field $\mathbb{F}_q$ of order $q$. A blocking set in $\mathrm{PG}(n,q)$ is a set of points that has non-empty intersection with…

Let $\cal P$ be a finite classical polar space of rank $d$. An $m$-regular system with respect to $(k - 1)$-dimensional projective spaces of $\cal P$, $1 \le k \le d - 1$, is a set $\cal R$ of generators of $\cal P$ with the property that…

A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space over $\mathbb{F}_q$ equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A…

The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…

Cameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this article we present the first two constructions of…

Combinatorial designs have been studied for nearly 200 years. Fifty years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their q-analogs, also known as subspace designs or designs over finite fields. Designs can be defined…

In this paper, we construct two infinite families of tight sets with parameters $(q^{2r-2}-1)$ and $(q^{2r-1}-q^{2r-2})$, respectively, in the Hermitian polar space $\mathcal{H}(2r-1,q^2)$ for any $r\ge 2$ and any prime power $q$. Both…

The size of the largest Erd\H os-Ko-Rado set of generators in the finite classical polar space is known for all polar spaces except for $H(2d-1,q^2)$ when $d\ge 5$ is odd. We improve the known upper bound in this remaining case by using a…

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically…

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…

The rank of a point-line geometry G is usually defined as the generating rank of G, namely the minimal cardinality of a generating set. However, when the subspace lattice of G satisfies the Exchange Property we can also try a different…

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

We find finite, reasonably small, generator sets of the coordinate rings of G-character varieties of finitely generated groups for all classical groups G. This result together with the method of Grobner basis gives an algorithm for…

Given polar spaces $(V,\beta)$ and $(V,Q)$ where $V$ is a vector space over a field $K$, $\beta$ a reflexive sesquilinear form and $Q$ a quadratic form, we have associated classical isometry groups. Given a subfield $F$ of $K$ and an…