Related papers: Quantized dual graded graphs

In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins…

The branching ratio is calculated for three different models of 2d gravity, using dynamical planar phi-cubed graphs. These models are pure gravity, the D=-2 Gaussian model coupled to gravity and the single spin Ising model coupled to…

It is well known that the Gauss map for a complex plane curve is birational, whereas the Gauss map in positive characteristic is not always birational. Let $q$ be a power of a prime integer. We study a certain plane curve of degree…

Let $S$ be a spinor bundle of a pseudo-Euclidean vector bundle $(E,\mathrm{g})$ of even rank. We introduce a new filtration on the algebra $\mathcal{D}(M,S)$ of differential operators on $S$. As main property, the associated graded algebra…

We introduce a generalization of the scaled relative graph (SRG) to pairs of operators, enabling the visualization of their relative incremental properties. This novel SRG framework provides the geometric counterpart for the study of…

We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations…

We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured…

We consider certain quotient algebras of tensor algebras of bimodules $M$ over a finite-dimensional algebra $R$, and we investigate Frobenius type properties of such algebras. Our main interest is in the case where $M=R^*$, the linear dual…

We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…

We consider signed graphs, i.e, graphs with positive or negative signs on their edges. We construct some families of bipartite signed graphs with only two distinct eigenvalues. This leads to constructing infinite families of regular…

We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\lambda)$ over a quantum generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and its…

This paper is devoted to qualgebras and squandles, which are quandles enriched with a compatible binary/unary operation. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. Topologically,…

We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing graph cohomology classes from a contractible differential…

Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…

We investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters…