Related papers: Maximum scattered $\mathbb{F}_q$-linear sets of $\…

We construct a random model to study the distribution of class numbers in special families of real quadratic fields $\mathbb Q(\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued…

In this paper, we construct a new family of $(q^4+1)$-tight sets in $Q(24,q)$ or $Q^-(25,q)$ according as $q=3^f$ or $q\equiv 2\pmod 3$. The novelty of the construction is the use of the action of the exceptional simple group $F_4(q)$ on…

We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.

A $\left(n,\ell,\gamma\right)$-sharing set family of size $m$ is a family of sets $S_1,\ldots,S_m\subseteq [n]$ s.t. each set has size $\ell$ and each pair of sets shares at most $\gamma$ elements. We let $m\left(n,\ell,\gamma\right)$…

We investigate the extremal properties of saturated partial plane embeddings of maximal planar graphs. For a planar graph $G$, the plane-saturation number $\mathrm{sat}_{\mathcal{P}}(G)$ denotes the minimum number of edges in a plane…

Let $\mathbb{F}_{q^2}$ be the finite field with $q^2$ elements. Most of the known $\mathbb{F}_{q^2}$-maximal curves arise as quotient curves of the $\mathbb{F}_{q^2}$-maximal Hermitian curve $\mathcal{H}_{q}$. After a seminal paper by…

Given a finite poset $\mathcal P$, how small can a family $\mathcal F$ of subsets of $[n]$ be such that $\mathcal F$ does not contain an induced copy of $\mathcal P$, but $\mathcal F\cup\{X\}$ contains such a copy for all $X\in\mathcal…

For two posets $P$ and $Q$, we say $Q$ is $P$-free if there does not exist any order-preserving injection from $P$ to $Q$. The speical case for $Q$ being the Boolean lattice $B_n$ is well-studied, and the optiamal value is denoted as…

We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices…

Julius Whiston and Jan Saxl showed that the size of an irredundant generating set of the group G=PSL(2,p) is at most four and computed the size m(G) of a maximal set for many primes. We will extend this result to a larger class of primes,…

New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for q <= 9109. From these new bounds it follows that for q <= 2621 and q = 2659,2663,2683,2693,2753,2801, the relation…

We complete the classification of the finite special linear groups $\SL_n(q)$ which are $(2,3)$-generated, i.e., which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple…

We prove that in dimension $n \ge 2$ the main singularities of a complex potential $q$ having a certain a priori regularity are contained in the Born approximation $q_\theta$ constructed from fixed angle scattering data. Moreover,…

We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p…

In this paper, we show that a small minimal k-blocking set in PG(n, q3), q = p^h, h >= 1, p prime, p >=7, intersecting every (n-k)-space in 1 (mod q) points, is linear. As a corollary, this result shows that all small minimal k-blocking…

There exists just one regular polytope of rank larger than 3 whose full automorphism group is a projective general linear group PGL_2(q), for some prime-power q. This polytope is the 4-simplex and the corresponding group is PGL_2(5), which…

For $p, q\in \mathbb{N}$, a finite nonempty set $F$ is said to be $(p,q)$-Schreier (or maximal $(p,q)$-Schreier, respectively) if $q\min F\ge p|F|$ (or $q\min F = p|F|$, respectively). For $n\in \mathbb{N}$, let $$\mathcal{S}^{p/q}_{n}\ :=\…

This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of given order and clique number. More precisely, let G be a graph of order n, let A be its adjacency matrix, and let D be the diagonal matrix…

We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of q-hypergeometric function of type ${_2}\phi_1$. The orthogonality measure is the wrapped…