Related papers: Graph complexes from the geometric viewpoint
Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…
We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…
In this paper we define 3-crossed modules for commutative (Lie) algebras and investigate the relation between this construction and the simplicial algebras. Also we define the projective 3-crossed resolution for investigate a higher…
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…
We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Using the orbicell decomposition of the Deligne-Mumford compactification of the moduli space of Riemann surfaces studied previously, a chain complex based on semistable ribbon graphs is constructed which is an extension of Konsevich's graph…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
Let $Z(\cal L)$ be the center of a Lie algebra $\cal L$ with Lie bracket $[\cdot, \cdot]$. %We then define The commuting graph of $\cal L$ is then defined by the simple undirected graph $\Gamma({\cal L})=(V_{\cal L},E_{\cal L})$ in which…
This manuscript synthesizes almost fifteen years of research in algebraic combinatorics, in order to highlight, theme by theme, its perspectives. In part one, building on my thesis work, I use tools from commutative algebra, and in…
Consider the real vector space of formal sums of non-empty, finite unoriented graphs without multiple edges and loops. Let the vertices of graphs be unlabelled but let every graph $\gamma$ be endowed with an ordered set of edges…
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with…
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…
During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolmogoroff and Gel'fand-Naimark, this branch developed as from…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…