INTRODUCTION
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Because of the macroscopic degeneracy of single-particle states in a Landau level, neither disorder nor electron-electron interactions in a two-dimensional electron system (2DES) can be treated perturbatively in the quantum Hall regime. This is the [*raison d’être*]{} for the many interesting and surprising phenomena[@general] which have arisen in quantum Hall physics. Theories of quantum Hall physics usually include either only interactions or only disorder, although both are always present. In particular, it is common to include only disorder in studies of the integer quantum Hall effect (IQHE), which generally focus on the sudden jump in the Hall conductivity between values separated by $e^2/h$, and it is common to include only interactions in studies of the fractional quantum Hall effect (FQHE), which generally focus on the ability of interactions to create charge gaps at partial Landau level fillings. The competition between interactions and disorder has often, but not always,[@Green; @Nederveen] been neglected, in part because of the lack of easily manageable analytical and numerical tools that can deal with both simultaneously. In this paper we address an instance in which this competition is particularly direct and can be successfully addressed with elementary techniques.

At Landau level filling factor $\nu=1$, 