Related papers: Electrical networks and hyperplane arrangements
Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex Delta_{A,H} as the subdivision of the link of A induced by H. In particular, this generalizes Steingrimsson's coloring…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…
Drawing parallels with hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection $\mathcal{A}$ of locally flat, codimension-1…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
This paper is about the combinatorics of finite point configurations in the tropical projective space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be…
This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis…
The optical properties of infinite planar array of scattering particles, metasurfaces and metagratings, are attracting special attention lately for their rich phenomenology, including both plasmonic and high-refractive-index dielectric…
Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich…
We study generating functions of strict and non-strict order polynomials of series-parallel posets, called order series. These order series are closely related to Ehrhart series and h*-polynomials of the associated order polytopes. We…
Discriminantal arrangements are hyperplane arrangements, which are generalized braid ones. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is…
The statistical tools of Complex Network Analysis are of great use to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
The aim of this note is a combinatorial description of a category of $D$-modules over an affine space, smooth along the stratification defined by an arrangement of hyperplanes. These $D$-modules are assumed to satisfy certain non-resonance…
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…
The enumeration of points on (or off) the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function. We discuss the basic…
We study the signalling structure of higher order quantum maps from an order-theoretic perspective, building on the combinatorial characterization of higher order types by Bisio and Perinotti. We have shown in a previous work…