Related papers: Semiovals in PG(2,8) and PG(2,9)

A {\em maximal partial ovoid} of a generalized quadrangle is a maximal set of points no two of which are collinear. The problem of determining the smallest size of a maximal partial ovoid in quadrangles has been extensively studied in the…

In the projective space $\mathrm{PG}(3,q)$, we consider 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 orbits.…

We consider the action of the $2$-dimensional projective special linear group $PSL(2,q)$ on the projective line $PG(1,q)$ over the finite field $\F_q$, where $q$ is an odd prime power. A subset $S$ of $PSL(2,q)$ is said to be an…

A spread of a Hermitian unital in PG(2,q^2) is a set of q^2+q+1 pairwise disjoint blocks that partition the points of the unital. In this paper, we discuss the results of an exhaustive computer search for spreads of Hermitian unitals of…

We introduce polyhedral cones associated with $m$-hemimetrics on $n$ points, and, in particular, with $m$-hemimetrics coming from partitions of an $n$-set into $m+1$ blocks. We compute generators and facets of the cones for small values of…

In this paper, we study the cardinality of the smallest set of lines of the finite projective spaces $\operatorname{PG}(n,q)$ such that every plane is incident with at least one line of the set. This is the first main open problem…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic…

Consider the complete convex geometric graph on $2m$ vertices, $CGG(2m)$, i.e., the set of all boundary edges and diagonals of a planar convex $2m$-gon $P$. In [C. Keller and M. Perles, On the Smallest Sets Blocking Simple Perfect Matchings…

In this paper we prove that a set of points $B$ of PG(n,2) is a minimal blocking set if and only if $<B>=PG(d,2)$ with $d$ odd and $B$ is a set of $d+2$ points of $PG(d,2)$ no $d+1$ of them in the same hyperplane. As a corollary to the…

In this paper, we study the explicit structure of the graded ring of elliptic modular forms for the congruence subgroup $\Gamma_0(N)$ with N=1,2,3,4,5,6,7,8,9,10,12,16,18,25. More precisely, making use of some relations between Fourier…

Let $n$ be a positive integer. Denote by $\mathrm{PG}(n,q)$ the $n$-dimensional projective space over the finite field $\mathbb{F}_q$ of order $q$. A blocking set in $\mathrm{PG}(n,q)$ is a set of points that has non-empty intersection with…

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes…

A regular polyhedron of type {p, q} has at least 2pq flags, and it is called tight if it has exactly 2pq flags. The values of p and q for which there exist tight orientably regular polyhedra were previously known. We determine for which…

In this paper, we characterise ovoidal cones by their intersection numbers. We first show that a set of points of $\mathrm{PG}(4,q)$ which intersects planes in $1$, $q+1$ or $2q+1$ points is either an ovoidal cone or a parabolic quadric,…

Hyperovals in $\PG(2,\gf(q))$ with even $q$ are maximal arcs and an interesting research topic in finite geometries and combinatorics. Hyperovals in $\PG(2,\gf(q))$ are equivalent to $[q+2,3,q]$ MDS codes over $\gf(q)$, called hyperoval…

S. Rottey and G. Van de Voorde characterized regular pseudo-ovals of PG(3n - 1, q), q = 2^h, h >1 and n prime. Here an alternative proof is given and slightly stronger results are obtained.

This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such…

A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of…

We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GL_n in characteristic p > 0. In particular, we compute the dimensions of the indecomposable tilting modules modulo p.

Our starting point is a very simple one, namely that of a set L_4 of four mutually skew lines in PG(7,2): Under the natural action of the stabilizer group G(L_4) < GL(8,2) the 255 points of PG(7,2) fall into four orbits omega_1, omega_2,…