Related papers: Flag-accurate arrangements
In 1989, Ziegler introduced the concept of a multi-arrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all…
Building on work of Brandt and Terao in their study of $k$-formality, we introduce a co-chain complex associated to a multi-arrangement and prove that its cohomologies determine freeness of the associated module of multi-derivations. This…
This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…
In his study of a Hochschild complex arising in connection with the free loop fibration, S. Saneblidze defined the freehedron, a certain polytope constructed via a truncation process from the hypercube. It was recently conjectured by F.…
In this paper, we propose a new solution for the detection problem of a coherent target in heterogeneous environments. Specifically, we first assume that clutter returns from different range bins share the same covariance structure but…
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…
We have previously proposed a study of arrangements of small circles which also surround regions in the plane realized as the images of natural real algebraic maps yielding Morse-Bott functions by projections. Among studies of arrangements,…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…
Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection…
We construct bundles $E_k(\A,\F) \to M$ over the complement $M$ of a complex hyperplane arrangement \A, depending on an integer $k \geq 1$ and a set $\F=\{f_1, \ldots, f_\mu\}$ of continuous functions $f_i \colon M \to \C$ whose differences…
In this paper, we revisit the old problem of compact finite difference approximations of the homogeneous Dirichlet problem in dimension 1. We design a large and natural set of schemes of arbitrary high order, and we equip this set with an…
We prove that for any automorphism $\alpha$ of a free group F of finite rank, one can efficiently compute a basis of the fixed point subgroup Fix(\alpha).
In this paper we study flag codes on $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Special attention is given to the connection between the parameters and properties of a flag code and the ones of a family of…
Recently, Cuntz and K\"uhne introduced a particular class of hyperplane arrangements stemming from a given graph $G$, so called connected subgraph arrangements $A_G$. In this note we strengthen some of the result from their work and prove…
We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…
Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left)…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…