Related papers: Convex domino towers
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.
We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings. These types of algebras arise naturally in the construction of Extended Affine Lie Algebras. The construction also gives…
It is demonstrated how the software system polymake can be used for computations in toric geometry. More precisely, counter-examples to conjectures related to A-determinants and defect polytopes are constructed.
Every right adjoint functor between presentable $\infty$-categories is shown to decompose canonically as a coreflection, followed by, possibly transfinitely many, monadic functors. Furthermore, the coreflection part is given a presentation…
We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Column-convex polyominoes are by now a well-explored model. So far, however, no attention has been given to polyominoes whose columns can have either one or two connected components. This little known kind of polyominoes seems not to be…
The deprojection of axisymmetric density distributions is generally indeterminate to within the addition of certain axisymmetric distributions (konus densities) that are invisible in projection. The known class of konus densities is…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical…
We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox…
We develop a quite elementary graph theoretic system for designing small-size augmented origami polyhedra out of Sonob\'e modules beginning with a (convex or not) deltahedron.
Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendicular to this direction. Suppose now that we can only get…
This paper presents a novel proof that for any convex cone, the size of conically independent generators is at most twice that of minimum cardinality generators. While this result is known for linear spaces, we extend it to general cones…
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
We prove a gluing theorem which allows to construct an ample divisor on a rational surface from two given ample divisors on simpler surfaces. This theorem combined with the Cremona action on the ample cone gives rise to an algorithm for…
We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by…
We provide a recipe to construct towers of fields producing high order elements in $\mathrm{GF}(q,2^n)$, for odd $q$, and in $\mathrm{GF}(2,2 \cdot 3^n)$, for $n \ge 1$. These towers are obtained recursively by $x_{n}^2 + x_{n} = v(x_{n -…
Extracting building contours from remote sensing imagery is a significant challenge due to buildings' complex and diverse shapes, occlusions, and noise. Existing methods often struggle with irregular contours, rounded corners, and…