Related papers: Exending pseudo-arcs in odd characteristic

A bipartite graph $G$ is semi-algebraic in $\mathbb{R}^d$ if its vertices are represented by point sets $P,Q \subset \mathbb{R}^d$ and its edges are defined as pairs of points $(p,q) \in P\times Q$ that satisfy a Boolean combination of a…

The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

In this paper, we generalize the so called Korchm\'aros--Mazzocca arcs, that is, point sets of size $q+t$ intersecting each line in $0, 2$ or $t$ points in a finite projective plane of order $q$. For $t\neq 2$, this means that each point of…

We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge),…

A subset of $\mathbb{F}_q^2$ is called an arc if it does not contain three collinear points. We show that there are at most $\binom{(1 + o(1))q}{m}$ arcs of size $m \gg q^{1/2} (\log q)^{3/2}$, nearly matching a trivial lower bound…

Let L be a simple Euclidean arrangement of n pseudolines. It is shown that if L has exactly one (>=5)=gon P, and k is the number of edges of P that are adjacent to an unbounded cell of the subarrangement of L induced by the pseudolines in…

In this paper we study a family of scattered $\F_q$--linear sets of rank $tn$ of the projective space $PG(2n-1,q^t)$ ($n \geq 1$, $t\geq 3$), called of {\it pseudoregulus type}, generalizing results contained in [G. Marino, O. Polverino, R.…

A strong arc decomposition of a digraph $D=(V,A)$ is a decomposition of its arc set $A$ into two disjoint subsets $A_1$ and $A_2$ such that both of the spanning subdigraphs $D_1=(V,A_1)$ and $D_2=(V,A_2)$ are strong. Let $T$ be a digraph…

A set without tangents in $\PG(2,q)$ is a set of points S such that no line meets S in exactly one point. An exterior set of a conic $\mathcal{C}$ is a set of points $\E$ such that all secant lines of $\E$ are external lines of…

A $t$-semiarc is a pointset ${\cal S}_t$ with the property that the number of tangent lines to ${\cal S}_t$ at each of its points is $t$. We show that if a small $t$-semiarc ${\cal S}_t$ in $\mathrm{PG}(2,q)$ has a large collinear subset…

In this paper we introduce generalized pseudo-quadratic forms and develope some theory for them. Recall that the codomain of a $(\sigma,\varepsilon)$-quadratic form is the group $\overline{K} := K/K_{\sigma,\varepsilon}$, where $K$ is the…

We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…

In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and…

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal…

We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…

Two graphs are said to be $Q$-cospectral if they share the same signless Laplacian spectrum. A simple graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if there exists no other non-isomorphic simple…

Let $Z\subset\mathbb{C}^N$ be an $n$-pseudoconcave subset, for $1\leq n<N$, which is locally the graph of a continuous function over a closed subset of $\mathbb{C}^n\times\mathbb{R}$. We show that $Z$ can be realised as the disjoint union…

Let $\mathrm{PG}(3,q)$ be the projective space of dimension three over the finite field with $q$ elements. Consider a twisted cubic in $\mathrm{PG}(3,q)$. The structure of the point-plane incidence matrix in $\mathrm{PG}(3,q)$ with respect…

We give an explicit description of the $q$-deformation of symplectic group $SP_{q}(2n)$ at the $C^*$-algebra level and find all irreducible representations of this $C^{*}$-algebra. Further we describe the $C^*$-algebra of the quotient space…