Related papers: The existence of subspace designs
Discussions of software design often refer to using "design spaces" to describe the spectrum of available design alternatives. This supports design thinking in many ways: to capture domain knowledge, to support a wide variety of design…
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…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilising the…
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
We investigate spherical 4-distance 7-designs by studying their distance distributions. We compute these distance distributions and use their product (an integer) to derive certain divisibility conditions relating the dimension $n$ and the…
Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden.…
Necessary and sufficient conditions are given for the existence of extended Schmidt decompositions, with more than two subspaces.
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common point. A triangle design is balanced if all points are…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…
We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no…
Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of…
Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given $k$ there is a minimal diameter of subsets at which there exists a covering with…
A basic problem in constant dimension subspace coding is to determine the maximal possible size ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in ${\bf F}_q^n$ such that the subspace distance satisfies…
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
Given any finite set of nonnegative integers, there exists a closed convex set whose facial dimension signature coincides with this set of integers, that is, the dimensions of its nonempty faces comprise exactly this set of integers. In…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…