Related papers: Large sets of complex and real equiangular lines
We say that two elements of a group or semigroup are $\Bbbk$-linear conjugates if their images under any linear representation over $\Bbbk$ are conjugate matrices. In this paper we characterize $\Bbbk$-linear conjugacy for finite semigroups…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.
We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related…
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.
Trilinear mappings appear naturally when performing spatial isogeometric discretizations of degree $p = 1$. Among them, birational maps are characterized by the property that both the mapping and the associated inverse map are rational and…
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line…
We develop techniques to split the principal parts on the projective line over an arbitrary ring and apply these techniques to give a complete classification of the principal parts on the projective line over any field of characteristic…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate is based on…
The image and the inverse image of a polyhedron under a linear transformation are polyhedrons.
We present a construction for complementary pairs of arrays that exploits a set of mutually-unbiased bases, and enumerate these arrays as well as the corresponding set of complementary sequences obtained from the arrays by projection. We…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a…
Resistive electrical networks constitute a beautiful example of open, interconnected, large-scale systems, giving rise to an elegant classical mathematical theory, still posing open problems and suggesting important extensions.
We study a special set of constellations of primes generated by twin primes.