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Ž w x. After their introduction in the 1940s cf. 18, the Hochschild homology and cohomology groups of an algebra with coefficients in a bimodule have played a fundamental role. Given an algebra and a-bimodule M and viewing both and M as left modules over the enveloping algebra e op Ž. sm, the Hochschild cohomology groups H*, M are the Ž. Ž. groups Ext*, M while the homology groups H#, M are the corre-Ž w x. sponding Tor groups cf. 5, Chap. IX. The most studied case has been that in which M s and, more specifically, when is a split basic finite dimensional algebra over a field K. In that case, the algebra is partially determined by combinatorial data, namely, its quiver with relations, and it Ž. Ž Ž.. is a natural goal to obtain information about H*, M resp. H#, M in terms of those combinatorial data. That was the scheme of the initial wx wx attempts made by Cibils 6 and Happel 17 to give explicit formulae for Ž. the dimensions of the H*,. In terms of computations, the first natural situation to look at is that in which the algebra is monomial, since