The C∗-algebra C∗(E) of a directed graph E is generated by partial isometries satisfying relations which reflect the path structure of the graph. In [10], Kumjian and Pask considered the action of a group G on C∗(E) induced by an action of G on E. They proved that if G acts freely and E is locally finite, then the crossed product C∗(E) × G is Morita equivalent to the C∗-algebra of the quotient ...

Calorons (periodic instantons) interpolate between monopoles and instantons, and their holonomy gives approximate Skyrmion configurations. We show that, for each caloron charge N ≤ 4, there exists a one-parameter family of calorons which are symmetric under subgroups of the three-dimensional rotation group. In each family, the corresponding symmetric monopoles and symmetric instantons occur as ...

In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by independence assumptions. In this work we initiate an effort to bridge this gap by developing tools that allow us to work with independence without assuming it. Let Gn be the set of all graphs on n vertices and let S be an arbitrary subset of Gn, e.g., the set of all gra...

Given a bowtie decomposition of the complete graph Kv admitting an automorphism group G acting transitively on the vertices of the graph, we give necessary conditions involving the rank of the group and the cycle types of the permutations in G. These conditions yield non–existence results for instance when G is the dihedral group of order 2v, with v ≡ 1, 9 (mod 12), or a group acting transitive...

We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix have at most one unit in the same position. In terms of Design Theory, such a matrix is an incidence matrix of a symmetric configuration. Also, it gives rise to an n-regular bipartite graphs without 4-cycles, which can be used for c...