Related papers: Decomposable Subspaces, Linear Sections of Grassma…
We define lines of minima in the thick part of Outer space for the free group Fn with n>2 generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully irreducible outer automorphism of Fn defines such…
For the category of group codes, that generalizes the category of linear codes over a finite field, and with the generalized notions of direct sums and ndecomposable group codes, we prove that every MDS non trivial code, every perfect non…
We explore the indecomposable submodule structure of quantum Grassmann super-algebra $\Omega_q(m|n)$ and its truncated objects $\Omega_q(m|n,\textbf{r})$ in the case when $q=\varepsilon$ is an $\ell$-th root of unity. A net-like…
We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower…
The set of all artin level quotients of a polynomial algebra in n variables having specified socle degree and type admits a parameter space. It is in fact a quasiprojective variety, naturally embedded in a Grassmannian. We give a geometric…
Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that…
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime which admits ADM decomposition is briefly discussed. We explicitly construct the…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide…
A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue…
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the…
A polynomial f (multivariate over a field) is decomposable if f = g(h) with g univariate of degree at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and an approximation to their number…
Let $Q$ be a quiver of extended Dynkin type $D$. In this first of two papers, we show that the quiver Grassmannian $Gr_e(M)$ has a decomposition into affine spaces for every dimension vector $e$ and every indecomposable representation $M$…
In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding $\varepsilon_k^{gr}$ of an orthogonal Grassmannian $\Delta_k$. In particular, we determine some of the parameters of the codes…
We consider the Grassman manifold $G(E)$ as the subset of all orthogonal projections of a given Euclidean space $E$ and obtain some explicit formulas concerning the differential geometry of $G(E)$ as a submanifold of $L(E,E)$ endowed with…
A univariate polynomial f over a field is decomposable if it is the composition f = g(h) of two polynomials g and h whose degree is at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and…
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the…
We construct two Lefschetz decompositions of the derived category of coherent sheaves on the Grassmannian of $k$-dimensional subspaces in a vector space of dimension $n$. Both of them admit a Lefschetz basis consisting of equivariant vector…
The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal ground spaces. In this paper we characterize the lattice…