Related papers: A combinatorial characterisation of embedded polar…
We establish that every embedding of a Grassmann graph in a polar Grassmann graph can be reduced to an embedding in a Grassmann graph or to an embedding in the collinearity graph of a polar space. Also, we consider $3$-embeddings, i.e.…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the…
We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our…
Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
Polarity is a fundamental reciprocal duality of $n$-dimensional projective geometry which associates to points polar hyperplanes, and more generally $k$-dimensional convex bodies to polar $(n-1-k)$-dimensional convex bodies. It is…
General criteria are given for when an embedding of a Mori dream space into another satisfies certain nice combinatorial conditions on some of their associated cones. An explicit example of such an embedding is studied.
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
This book is dedicated to Grassmannians associated with buildings of classical types: usual, polar, and half-spin Grassmannians. Grassmannians of vector spaces and Grassmannians consisting of totally isotropic subspaces of non-degenerate…
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally…
Based on SDSS data, we have considered the spatial environment of galaxies with extended polar rings. We used two approaches: estimating the projected distance to the nearest companion and counting the number of companions as a function of…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a…
We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated…
A statistical study of the environment around Polar Ring Galaxies is presented. Two kinds of search are performed: 1) a study of the concentration and diameters of all the objects surrounding the Polar Rings, within a search field 5 times…
Crossed electric and magnetic fields influence dipolar neutral particles in the same way as the magnetic field influences charged particles. The effect of crossed fields is proportional to the dipole moment of the particle (inherent or…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
In embedding calculus, spaces of embeddings are identified with derived mapping spaces between framed Fulton-MacPherson-type modules (framed configuration spaces). Unfortunately, there are no sufficiently good algebraic models for framed…
The polarized component of the diffuse radio synchrotron emission of our Galaxy shows structure, which is apparently unrelated to the structure in total intensity, on many scales. The structure in the polarized emission can be due to…