Related papers: Flag-accurate arrangements
We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there…
The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups $G(r,r,3)$ for $r \ge 3$ give rise to nice…
In the study of free arrangements, the most useful result to construct/check free arrangements is the addition-deletion theorem. Recently, the multiple version of the addition theorem is proved, called the multiple addition theorem (MAT) to…
Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
We study algebraic and homological properties of facet ideals of order complexes of posets which we call ideals of maximal flags of posets or simply flag ideals. We characterize the unmixed and Cohen-Macaulay flag ideals of graded posets.…
A number which is either the square of an integer or two times the square of an integer is called squarish. There are two main results in the literature on graphs whose number of perfect matchings is squarish: one due to Jockusch (for…
In this paper, we introduce the notion of a complete hypertetrahedral arrangement $\mathcal{A}$ in $\mathbb{P}^{n}$. We address two basic problems. First, we describe the local freeness of $\mathcal{A}$ in terms of smaller complete…
Let alpha = (a,b,...) be a composition. Consider the associated poset F(alpha), called a fence, whose covering relations are x_1 < x_2 < ... < x_{a+1} > x_{a+2} > ... > x_{a+b+1} < x_{a+b+2} < ... . We study the associated distributive…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
Absolute Parallelism (AP) has many interesting features: large symmetry group of equations; field irreducibility with respect to this group; vast list of consistent second order equations not restricted to Lagrangian ones. There is the…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
Let $\A$ be a free arrangement of $d$ lines in the complex projective plane, with exponents $d_1\leq d_2$. Let $m$ be the maximal multiplicity of points in $\A$. In this note, we describe first the simple cases $d_1 \leq m$. Then we study…
(Abridged abstract) For a finite real reflection group W and a W-orbit O of flats in its reflection arrangement---or equivalently a conjugacy class of its parabolic subgroups---we introduce a statistic on elements of W. We then study the…
Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type $\mathcal{A}_\mathcal{I}$ stemming from an ideal $\mathcal{I}$ in the set of positive roots of a…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
A new result of G. Cz\'edli states that for an ordered set $P$ with at least two elements and a group $G$, there exists a bounded lattice $L$ such that the ordered set of principal congruences of $L$ is isomorphic to $P$ and the…
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…
A graph $\Gamma$ is $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. If $V(\Gamma)$ admits a nontrivial $G$-invariant partition ${\cal B}$ such…
A flag matroid can be viewed as a chain of matroids linked by quotients. Flag matroids, of which relatively few interesting families have previously been known, are a particular class of Coxeter matroids. In this paper we give a family of…