Related papers: Cameron-Liebler line classes in ${\rm PG}(3,5)$
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…
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…
We construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$.
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,…
A {\it Cameron -- Liebler line class} ${\cal L}$ with parameter $x$ is a set of lines of projective geometry $PG(3,q)$ such that each line of ${\cal L}$ meets exactly $x(q+1)+q^2-1$ lines of ${\cal L}$ and each line that is not from ${\cal…
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…
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…
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…
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…
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…
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…
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 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…
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…
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…
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,…
In this work we deal with the class of nonlinear (p,q)-Laplacian system. Non-existence results of positive weak solutions for this system are established.
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…
In this work, we prove the existence of maximal partial line spreads in PG(5,q) of size q^3+q^2+kq+1, with 1 \leq k \leq (q^3-q^2)/(q+1), k an integer. Moreover, by a computer search, we do this for larger values of k, for q \leq 7. Again…
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…