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The following partition problem was first introduced by R.C. Entringer and has subsequently been studied by the first author and more recently by Bollobás and Scott, who consider the hypergraph version as well, using a probabilistic technique. The partition problem is that of coloring the vertex set of a graph with s colors so that the number of induced(More)
In this paper we give a construction of free 2-crossed modules. By the use of a `step-by-step' method based on the work of Andr e, we will give a description of crossed algebraic models for the steps in the construction of a free simplicial resolution of an algebra. This involves the introduction of the notion of a free 2-crossed module of algebras.
The category of crossed complexes gives an algebraic model of CW-complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the(More)
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