Related papers: A note on Cameron - Liebler line classes in PG(n,4…
New examples of Cameron-Liebler line classes in $\mathrm{PG}(3,q)$ are given with parameter $\frac{1}{2}(q^2 -1)$. These examples have been constructed for many odd values of $q$ using a computer search, by forming a union of line orbits…
The study of Cameron-Liebler line classes in PG($3,q$) arose from classifying specific collineation subgroups of PG($3,q$). Recently, these line classes were considered in new settings. In this point of view, we will generalize the concept…
In this paper we describe an infinite family of Cameron-Liebler line classes of ${\rm PG}(3,q)$ with parameter $(q^2 + 1)/2$, $q\equiv 1\pmod{4}$. The example obtained admits ${\rm PGL}(2,q)$ as an automorphism group and it is shown to be…
In this article we study Cameron-Liebler line classes in PG$(n,q)$ and AG$(n,q)$, objects also known as boolean degree one functions. A Cameron-Liebler line class $\mathcal{L}$ is known to have a parameter $x$ that depends on the size of…
Cameron-Liebler line classes were introduced in \cite{CL}, and motivated by a question about orbits of collineation groups of $\PG(3,q)$. These line classes have appeared in different contexts under disguised names such as Boolean degree…
We complete a classification of Cameron-Liebler line classes in ${\rm PG}(3,5)$, and show in a uniform way all non-existence results for those in ${\rm PG}(3,q)$, $q\leq 5$.
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 paper, we give an algebraic construction of a new infinite family of Cameron-Liebler line classes with parameter $x=\frac{q^2-1}{2}$ for $q\equiv 5$ or $9\pmod{12}$, which generalizes the examples found by Rodgers in \cite{rodgers}…
Cameron-Liebler line classes and Cameron-Liebler k-classes in PG(2k+1,q) are currently receiving a lot of attention. Links with the Erd\H{o}s-Ko-Rado results in finite projective spaces occurred. We introduce here in this article the…
We study Cameron-Liebler $k$-sets in the affine geometry, so sets of $k$-spaces in $\text{AG}(n, q)$. This generalizes research on Cameron-Liebler $k$-sets in the projective geometry $\text{PG}(n, q)$. Note that in algebraic combinatorics,…
Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F. Ihringer. We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in…
In this article we generalize the concepts that were used in the PhD thesis of Drudge to classify Cameron-Liebler line classes in PG$(n,q), n\geq 3$, to Cameron-Liebler sets of $k$-spaces in PG$(n,q)$ and AG$(n,q)$. In his PhD thesis,…
In this paper, we describe a new infinite family of $\frac{q^{2}-1}{2}$-tight sets in the hyperbolic quadrics $\mathcal{Q}^{+}(5,q)$, for $q \equiv 5 \mbox{ or } 9 \bmod{12}$. Under the Klein correspondence, these correspond to…
An $m$-$cover$ of lines of a finite projective space ${\rm PG}(r,q)$ (of a finite polar space $\cal P$) is a set of lines $\cal L$ of ${\rm PG}(r,q)$ (of $\cal P$) such that every point of ${\rm PG}(r,q)$ (of $\cal P$) contains $m$ lines of…
We consider the problem of classifying the lines of the projective $3$-space $PG(3,q)$ over a finite field $\mathbb{F}_q$ into orbits of the group $PGL_2(q)$ of linear symmetries of the twisted cubic $C$. The problem has been solved in…
This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\mathrm{PG}(n,q)$ or $\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size…
We investigate Cameron-Liebler sets of planes in the Klein quadric $Q^+(5,q)$ in PG$(5,q)$. We prove that there are many examples of such Cameron-Liebler sets of planes in the Klein quadric. More specifically, we provide an incomplete list…
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…
Over any field $\mathbb K$, there is a bijection between regular spreads of the projective space ${\rm PG}(3,{\mathbb K})$ and $0$-secant lines of the Klein quadric in ${\rm PG}(5,{\mathbb K})$. Under this bijection, regular parallelisms of…
In this paper we study combinatorial invariants of the equivalence classes of pencils of cubics on $\mathrm{PG}(1,q)$, for $q$ odd and $q$ not divisible by 3. These equivalence classes are considered as orbits of lines in…