Amalgamations and link graphs of Cayley graphs.
Amenability and Ramsey theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
Amenability and Ramsey theory in the metric setting
Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a condition.
Amenability, unimodularity, and the spectral radius of random walks on finite graphs.
Amenable group actions on infinite graphs.
Amenable groups and cellular automata
We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...
Amply regular graphs and block designs.
An algebraic characterization of geodetic graphs
We say that a binary operation is associated with a (finite undirected) graph (without loops and multiple edges) if is defined on and if and only if , and for any , . In the paper it is proved that a connected graph is geodetic if and only if there exists a binary operation associated with which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).
An algebraic framework of weighted directed graphs.
An algebraic summation over the set of partitions and some strange evaluations
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...
An algorithm for optimal partitioning of a graph
An Algorithm for Scaling Matrices and Computing the Minimum Cycle Mean in a Digraph.
An algorithm for the decomposition of ideals of the group ring of a symmetric group.
An algorithm to construct greedy drawings of triangulations.
An Algorithm To Recognize A Generalized Line Graph And Output It's Root Graph
An algorithmic Friedman-Pippenger theorem on tree embeddings and applications.
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.
An almost naive algorithm for finding relative neighbourhood graphs in metrics