Related papers: Optimal line packings from finite group actions
We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over…
We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…
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…
The goal of this article is to exhibit two new families of finitely generated simple groups of homeomorphisms of $\mathbf{R}$. These families are strikingly different from existing families owing to the nature of their actions on…
We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
An equiangular tight frame (ETF) yields a type of optimal packing of lines in a Euclidean space. ETFs seem to be rare, and all known infinite families of them arise from some type of combinatorial design. In this paper, we introduce a new…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be embedded in projective space as line arrangements. We…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…