Related papers: Semiarcs with a long secant in $\mathrm{PG}(2,q)$
Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and…
Menger's theorem tells us that if $S,T$ are sets of vertices in a graph $G$, then (for $k\ge0$) either there are $k+1$ vertex-disjoint paths between $S$ and $T$, or there is a set of $k$ vertices separating $S$ and $T$. But what if we want…
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line, or block, is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points…
This paper is focused on numerical semigroups and presents a simple construction, that we call dilatation, which, from a starting semigroup $S$, permits to get an infinite family of semigroups which share several properties with $S$. The…
Let $\mathcal{T}$ be a set of $n$ flat (planar) semi-algebraic regions in $\mathbb{R}^3$ of constant complexity (e.g., triangles, disks), which we call plates. We wish to preprocess $\mathcal{T}$ into a data structure so that for a query…
A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set $K$ of the Desarguesian plane $PG(2,q)$ is obtained. The case where $K$ is a maximal $(k,n)$-arc is considered to greater extent.
In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting…
To an arc $\mathcal{A}$ of $\mathrm{PG}(k-1,q)$ of size $q+k-1-t$ we associate a tensor in $\langle \nu_{k,t}(\mathcal{A})\rangle^{\otimes k-1}$, where $\nu_{k,t}$ denotes the Veronese map of degree $t$ defined on $\mathrm{PG}(k-1,q)$. As a…
The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to…
A partial $(n,k,t)_\lambda$-system is a pair $(X,\mathcal{B})$ where $X$ is an $n$-set of vertices and $\mathcal{B}$ is a collection of $k$-subsets of $X$ called blocks such that each $t$-set of vertices is a subset of at most $\lambda$…
The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C). In the construction there appears a sign…
In this paper, we introduce the graph $G(S)$ of a bounded semilattice $S$, which is a generalization of the intersection graph of the substructures of an algebraic structure. We prove some general theorems about these graphs; as an example,…
We enumerate height-restricted path diagrams associated with $q$-tangent and $q$-secant numbers by considering convergents of continued fractions, leading to expressions involving basic hypergeometric functions. Our work generalises some…
We give a combinatorial characterization of the family of lines of P G(3, q) which meet a hyperbolic quadric in two points (the so called secant lines) using their intersection properties with the points and planes of PG(3,q).
We consider the features of multiparticle tree cross sections in scalar theories in the framework of a semiclassical approach. These cross sections at large multiplicities have exponential form, and the properties of the exponent in…
Two plane analytic branches are topologically equivalent if and only if they have the same multiplicity sequence. We show that having same semigroup is equivalent to having same multiplicity sequence, we calculate the semigroup from a…
In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…
Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$, with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd, then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq t(T)…
In this paper we describe the structure of the tangent cone of a numerical semigroup ring $A=k[[S]] \subseteq k[[t]]$ with multiplicity $e$ (as a module over the Noether normalization determined by the fiber cone of the ideal generated by…
A {\em pseudo-arc} in $\mathrm{PG}(3n-1,q)$ is a set of $(n-1)$-spaces such that any three of them span the whole space. A pseudo-arc of size $q^n+1$ is a {\em pseudo-oval}. If a pseudo-oval $\mathcal{O}$ is obtained by applying field…