Related papers: Path homology of circulant digraphs

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

We say that a Hamilton cycle $C=(x_1,\ldots,x_n)$ in a graph $G$ is $k$-symmetric, if the mapping $x_i\mapsto x_{i+n/k}$ for all $i=1,\ldots,n$, where indices are considered modulo $n$, is an automorphism of $G$. In other words, if we lay…

We discuss a graph complex formed by directed acyclic graphs with external legs. This complex comes in particular with a map to the ribbon graph complex computing the (compactly supported) cohomology of the moduli space of points $\mathcal…

Acting on operators with a bare dimension $\Delta\sim N^2$ the dilatation operator of $U(N)$ ${\cal N}=4$ super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the…

The minimal degree of a permutation group $G$ is the minimum number of points not fixed by non-identity elements of $G$. Lower bounds on the minimal degree have strong structural consequences on $G$. In 2014 Babai proved that the…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalizaton group are small, we…

Let Y be a compact Riemann surface, phi:Y -> CP^1 a meromorphic function, and Gamma in Y a ribbon graph avoiding the critical points of phi. Then phi(Gamma) is an immersed graph in CP^1. Conversely, given an immersion im:Theta to bCP^1 of…

We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…

This paper investigates, in the context of discrete-time switching systems, the problem of comparison for path-complete stability certificates. We introduce and study abstract operations on path-complete graphs, called lifts, which allow us…

The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge…

With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants associated with topological quantum field theories of pseudoholomorphic maps can be computed…

Let $G$ be a graph with vertex set $V(G)$, $f$ a permutation of $V(G)$. Define $\delta_f(G)=|d(x,y)-d(f(x),f(y))|$ and $\delta_f(G)=\Sigma\delta_f(x,y)$, where the sum is taken over all unordered pair $x$, $y$ of distinct vertices of $G$.…

An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$ from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by…

We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…

Being motivated in terms of mathematical concepts from the theory of electrical networks, Klein & Ivanciuc introduced and studied a new graph-theoretic cyclicity index--the global cyclicity index (Graph cyclicity, excess conductance, and…

From a generalization to $Z^n$ of the concept of congruence we define a family of regular digraphs or graphs called multidimensional circulants, which turn out to be Cayley (di)graphs of Abelian groups. This paper is mainly devoted to show…

A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…

We continue the study of the $k$-cut complex $\Delta_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jeli\'c Milutinovi\'c, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2):…

We establish several useful commutative diagrams consisting of low term exact sequences attached to {\Grot} spectral sequences, which extends and integrates the previous ones appeared in literature such as Alexei~N. Skorobogatov [Beyond the…