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- Alan F. Beardon
- Australasian J. Combinatorics
- 2004

There are many results on edge-magic, and vertex-magic, labellings of finite graphs. Here we consider magic labellings of countably infinite graphs over abelian groups. We also give an example of a finite connected graph that is edge-magic over one, but not over all, abelian groups of the appropriate order.

- Alan F. Beardon
- Discrete Applied Mathematics
- 2013

- A. F. Beardon
- 1996

This paper contains some tentative steps towards describing the structure of non-discrete subgroups of SL(2; R). The main idea is that if a one-parameter family of groups G z varies analytically with the parameter z , then, using analytic continuation, certain results about discrete groups can be analytically continued to those groups in the family that are… (More)

- A. F. Beardon
- 2006

The goal is to present an introduction to the hyperbolic metric and various forms of the Schwarz-Pick Lemma. As a consequence we obtain a number of results in geometric function theory.

- Alan F. Beardon, Kathy Driver
- Journal of Approximation Theory
- 2005

- Dov Aharonov, Alan F. Beardon, Kathy Driver
- The American Mathematical Monthly
- 2005

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17–38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example… (More)

We show that if a pair of meromorphic functions parametrize an algebraic curve then they have a common right factor, and we use this to derive a variety of results on algebraic curves.

By using the theory of elliptic integrals we give an exact formula for the hyperbolic density of a rectangle at its centre. We compare this to the hyperbolic density of an infinite strip and obtain (in this special case) a quantitative version of the Carathéodory Kernel Theorem.