Related papers: Pattern Recognition on Oriented Matroids: Symmetri…

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary…

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies…

We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.

We introduce the subsemigroup complex of a finite semigroup S as a (boolean representable) simplicial complex defined through chains in the lattice of subsemigroups of S. We present a research program for such complexes, illustrated through…

We investigate the mutual relations between the centers of different elements in the deconstruction lattice of a 2D conformal model, and show how these can be described using exact sequences of abelian groups. In particular, we exhibit a…

In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…

The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

For a symmetric 2t-cycle in the tope graph of a simple oriented matroid M on the ground set {1,...,t}, where t is even, we describe decompositions of topes and subtopes of M with respect to the subtopes corresponding to the edges of the…

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

In problem-solving, a path towards solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of…

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…

In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…

In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…