Related papers: Hyperplane Sections, Groebner Bases, and Hough Tra…

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…

This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…

Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm…

The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…

Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\Bbb Z[X]$, $X=(x_1,\dots,x_n)$ and let $I$ be their union. We propose an algorithm to compute the Gr\"obner base of $I$ under the assumption that the…

In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel…

In each of the three projective planes coordinatised by the Knuth's binary semifield $\mathbb{K}_n$ of order $2^n$ and two of its Knuth derivatives, we exhibit a new family of infinitely many translation hyperovals. In particular, when…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

Hilbert schemes of suitable smooth, projective 3-fold scrolls over the Hirzebruch surface F_e, with e > 1, are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the…

Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given

In a previous paper, the author compute the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal…

Any compact body in ${\mathbb R}^N$ with smooth boundary defines a two-valued function on the space of affine hyperplanes: the volumes of two parts into which these hyperplanes cut the body. This function is never algebraic if $N$ is even…

We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…

Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

Many algorithms require discriminative boundaries, such as separating hyperplanes or hyperballs, or are specifically designed to work on spherical data. By applying inversive geometry, we show that the two discriminative boundaries can be…