Related papers: The spectral problem and algebras associated with …
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the…
I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce…
This paper studies silted algebras, namely, endomorphism algebras of 2-term silting complexes, over path algebras of Dynkin quivers. We will describe an algorithm to produce all basic 2-term silting complexes over the path algebra of a…
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral…
In this paper, we discuss a method of constructing separable representations of the $C^*$-algebras associated to strongly connected row-finite $k$-graphs $\Lambda$. We begin by giving an alternative characterization of the…
In this paper we show how to produce a large number of representations of a graph C*-algebra in the space of the bounded linear operators in $L^2(X,\mu)$. These representations are very concrete and, in the case of graphs that satisfy…
Motivated by the harmonic analysis of self-affine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row…
Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between \emph{optimization} and…
We consider some problems concerning the maximum number of (strong) dominating sets in a regular graph, and their weighted analogues. Our primary tool is Shearer's entropy lemma. These techniques extend to a reasonably broad class of graph…
The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…
Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
The goal of the paper is to apply the general operator theoretic construction known as the Schur complement for computation of the spectrum of certain infinite graphs which can be viewed as finite graphs with the ray attached to them. The…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…