Related papers: Partial spreads and vector space partitions
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, K\"uhn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in…
Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium…
A spherical three-distance set is a finite collection $X$ of unit vectors in $\mathbb{R}^{n}$ such that for each pair of distinct vectors has three inner product values. We use the semidefinite programming method to improve the upper bounds…
We study nested partitions of $R^d$ obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition of this kind and then distributing…
In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called…
Polar spaces over finite fields are fundamental in combinatorial geometry. The concept of polar space was firstly introduced by F. Veldkamp who gave a system of 10 axioms in the spirit of Universal Algebra. Later the axioms were simplified…
After a discussion of the Griesmer and Heller bound for the distance of a convolutional code we present several codes with various parameters, over various fields, and meeting the given distance bounds. Moreover, the Griesmer bound is used…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.
Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the…
We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…