Interlocked permutations

The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our results are purely combinatorial and in line with previous work of the third author about permutation capacity.Comment: 8 page

Lipschitz null-homotopy of mappings S3→S2S^3 \rightarrow S^2

One of the open problems in quantitative topology is as follows. Given homotopic mappings $f_0,f_1: S^m\rightarrow S^n$ of Lipschitz constant $L$ build the (asymptotically) simplest homotopy $f_\bullet: S^m\times[0,1]\rightarrow S^n$ between them. The present paper resolves this problem for the first formerly open case $m=3$, $n=2$ constructing a homotopy $f_\bullet$ with Lipschitz constant $O(L)$.Comment: 30 pages, 19 figures Added and corrected abstract, expanded acknowledgement

A Systematic Study of Symmetry Properties of Graphs I. Petersen Graph

Recently (Chem. Phys. Lett. 42 283 (1976) a simple procedure for deriving symmetry properties of graphs has been suggested. It is based on a canonical numbering of the vertices of a graph, and consists in searching for all the acceptable numberings which have a unique adjacency matrix. In the series of papers initiated here we will apply the above procedure and derive all symmetry operations for graphs of interest to chemistry. We start with the Petersen graph which is of interest in discussions of isomerizations of trigonal bipyramidal structures

National and transnational structuring of the British corporate elite

Corporate power in Britain is multifaceted, multilayered and geographically structured. In contrast to the classic rise of the capitalist class, the established landed aristocracy was not overthrown in Britain but became embedded in its ascendancy, an articulation that strongly marks institutional forms of power to this day (Anderson 1964). The industrial revolution that drove the accumulation of national wealth in nineteenth-century Britain had its catalyst in the wealth of international trade and plunder, and in turn was quickly followed by international corporate expansion. British capital dominated international investment through to the Second World War and today still accounts for the world’s second largest overseas direct investment stock (Dunning and Archer 1987; United Nations Conference on Trade and Development 2011). So the British corporate elite are intimately structured by a complex of national and transnational influences. Periodic attempts to delve into the growing documentary archive of elite relationships in Britain have barely pierced the outer layers of the structures of corporate elite cohesion, however. The availability of data and the potentially strategic importance of a director’s role have led attention primarily towards interlocking directorships (Aaronovitch 1956; Useem 1984; Windolf 2002), while the mining of biographical databases provides an entry-point into elite schools, clubs and social circles (Sampson 1962). But these are only limited components of the taxonomy of multiple layers of inter-organizational bonds proposed by Scott and Griff (1984) as constituting elite cohesion, let alone extended to national and transnational dimensions (see Table 8.1). This chapter takes a modest taxonomic step through these layers, reviewing and extending John Scott’s periodic studies (1986, 1991a, 1991b, 2003; Scott and Griff 1984) of British director interlocks, temporarily and methodologically, and then considers the pattern of interlocks in the context of transnational influences on the British economy

Homology of the mapping class group for surfaces of genus 2 with boundary

We report on the computation of the integral homology of the mapping class group of genus g surfaces with one boundary curve and m punctures, when 2g + m is smaller than 6. In particular, it includes the genus 2 case with no or one puncture.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200