Related papers: A Note on Affinely Regular Polygons
In this paper, we consider point sets of finite Desarguesian planes whose multisets of intersection numbers with lines is the same for all but one exceptional parallel class of lines. We call such sets regular of affine type. When the lines…
We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them…
The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.
In this paper for any dimension n we give a complete list of lattice convex polytopes in R^n that are regular with respect to the group of affine transformations preserving the lattice.
We study the plane automorphisms given by polynomials with certain degree decompositions.
In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…
This is a systematic study of the behaviour of finite coverings of (affine) schemes with regard to two Grothendieck topologies: the canonical topology and the fpqc topology. The history of the problem takes roots in the foundations of…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of translates of a fixed lattice, we take a more general…
We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane…
Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite…
In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We prove the meromorphic continuation of the resolvent of the…
We address the question of identifying non-smooth points in affine real algebraic varieties. A simple algebraic criterion will be formulated and proven. As an application we can answer several questions about the configuration spaces of…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many…
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and…
Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…
We present some results about the number of rational points on a certain family of curves defined over a finite field. In a small number of cases the curves have more rational points than expected. Fibonacci numbers make an appearance, as…