相关论文: Constructions of Grassmannian Simplices

By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are constructed, some of which are shown to be optimal packings. A…

We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum…

We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the authors use maximal affine block designs and maximal sets of…

In this paper, we present a new construction of simplicial complexes of subpolynomial degree with arbitrarily good local spectral expansion. Previously, the only known high-dimensional expanders (HDXs) with arbitrarily good expansion and…

The desirable properties when constructing collections of subspaces often include the algebraic constraint that the projections onto the subspaces yield a resolution of the identity like the projections onto lines spanned by vectors of an…

A remarkable coincidence has led to the discovery of a family of packings of (m^2+m-2) m/2-dimensional subspaces of m-dimensional space, whenever m is a power of 2. These packings meet the ``orthoplex bound'' and are therefore optimal.

This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is…

In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters…

The paper deals with the solution of Shevrin ans Sapir problem. Infinite finitely presented nilsemigroup is constructed. The construction is based on aperiodic tilings, Goodman-Strauss type theorems on uniformly elliptic space. Space is…

It is often of interest to identify a given number of points in projective space such that the minimum distance between any two points is as large as possible. Such configurations yield representations of data that are optimally robust to…

We use group schemes to construct optimal packings of lines through the origin. In this setting, optimal line packings are naturally characterized using representation theory, which in turn leads to a necessary integrality condition for the…

We construct complete, embedded minimal annuli asymptotic to vertical planes in the Riemannian 3-manifold PSL. The boundary of these annuli consists of 4 vertical lines at infinity. They are constructed by taking the limit of a sequence of…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…

In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…

We define the notion of an approximate triangulation for a manifold $M$ embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in $M$ and use persistent homology to find a complex…

We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link graphs in the plane that are compatible at the edges and they…

We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…

We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local configuration space is built out of the poset of poset structures…