Related papers: Finite projective planes and the Delsarte LP-bound
In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.
A Delaunay polytope $P$ is said to be {\em extreme} if the only (up to isometries) affine bijective transformations $f$ of $\R^n$, for which $f(P)$ is again a Delaunay polytope, are the homotheties. This notion was introduced in…
For all finite fields of order up to $2^{30}$, we computationally prove that there are no planar monomials besides the ones already known.
We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to $3 \pmod{6}$. The only previously known examples have order $15$ or $21$.
There doesn't exists a finite planar map with all edges having the same length, and each vertex on exactly 5 edges.
We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order $k$ exist, for all $k\leq 11$, and we present a general existence result that holds for…
In spite of a recent breakthrough on upper bounds of the size of cap sets (by Croot, Lev and Pach (2017) and Ellenberg and Gijswijt (2017)), the classical cap set constructions had not been affected. In this work, we introduce a very…
In this article we present the largest set of unitals (totally 553) in projective planes of order 16. An open question is what is the number of the known unitals that are non-isomorphic to the reported ones. The results are obtained with a…
We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.
In this paper, first we obtain some new and interesting results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally of finite type projective module is continuous with…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…
Let $T_n(q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F(q)$ of order $q \geq 2$ and let ${^2T_n(q)}$ denote its free left module. For $n=2,3$ it is shown that the projective line over…
The numbers of $\mathbb{F}_q$-points of nonsingular hypersurfaces of a fixed degree in an odd-dimensional projective space are investigated, and an upper bound for them is given. Also we give the complete list of nonsingular hypersurfaces…
A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…
We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and can be generalized to arbitrary smooth projective curves.…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists, but not unique,…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
We introduce and study integral planes associated with crystallographic and non-crystallographic integral systems in real composition algebras. For an integral order $\Order$ in such an algebra we define the plane $\Order^{2}$ with…