Related papers: Derivation of Cameron-Liebler line classes

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

We introduce a class of permutation polynomial over $\mathbb F_{q^n}$ that can be written in the form $\frac{L(x)}{x^{q+1}}$ or $\frac{L(x^{q+1})}x$ for some $q$-linear polynomial $L$ over $\mathbb F_{q^n}$. Specifically, we present those…

In this paper we show there exists an infinite family of number fields $L$, Galois over $\mathbb{Q}$, for which the smallest prime $p$ of $\mathbb{Q}$ which splits completely in $L$ has size at least $( \log(|D_L|) )^{2+o(1)}$. This gives a…

We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…

We prove that the parameter $x$ of a tight set $\mathcal{T}$ of a hyperbolic quadric $\mathsf{Q}^+(2n+1,q)$ of an odd rank $n+1$ satisfies ${x\choose 2}+w(w-x)\equiv 0\mod q+1$, where $w$ is the number of points of $\mathcal{T}$ in any…

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+\gamma\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional…

Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…

In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. It is well known that the lines can be partitioned into classes every of which is a union of line orbits. All types…

A line packing is optimal if its coherence is as small as possible. Most interesting examples of optimal line packings are achieving equality in some of the known lower bounds for coherence. In this paper two infinite families of real and…

Using a general $q$-series expansion, we derive some nontrivial $q$-formulas involving many infinite products. A multitude of Hecke--type series identities are derived. Some general formulas for sums of any number of squares are given. A…

In this paper we generalize constructions in two recent works of Ding, Heng, Zhou to any field $\mathbb{F}_q$, $q$ odd, providing infinite families of minimal codes for which the Ashikhmin-Barg bound does not hold.

In this paper, we prove new Liouville type results for a nonlinear equation involving infinity Laplacian with gradient of the form $$\Delta^\gamma_\infty u + q(x)\cdot \nabla{u} |\nabla{u}|^{2-\gamma} + f(x, u)\,=\,0\quad \text{in}\;…

In this paper, we construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conjecture.

We construct exceptional sequences of line bundles of maximal length on a family of surfaces isogenous to a higher product of unmixed type with $p_g=q=0$.

We constuct a family of hemisystems of the parabolic quadric $\mathcal{Q}(2d, q)$, for all ranks $d \ge 2$ and all odd prime powers $q$, that admit $\Omega_3(q) \cong \mathrm{PSL}_2(q)$. This yields the first known construction for $d \ge…

In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line…

The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…

In this paper we present a new class of perfect nonlinear %Dembowski-Ostrom polynomials over $\mathbb{F}_{p^{2k}}$ for any odd prime $p$. In addition, we show that the new perfect nonlinear functions are CCZ-inequivalent to all the…