Abstract
The essence of this paper lies in the appendix where we classify families of objects ranging from Douglas Rogers' bushes to Henry Finucan's folder stacks according to the way in which these families are generated. Objects in each family have certain features and our generation procedure is selected so that the question ‘how many objects are there with a prescribed number of features of each kind?’ can be rephrased ‘how many objects are generated by a prescribed number of partial operations of each kind?’
We deduce the answer to this question for arbitrary freely generated universal algebras from an array of Raney's. We find that a wide range of families of objects can be viewed as such algebras or subsets thereof obtained by appropriately restricting or colouring the generation procedure. We investigate relationships between the procedures generating these families and deduce relationships between the arrays answering the question above for each procedure.
Our message is that a classification by generation procedure is a useful tool in arranging the combinatorial information which has been amassed concerning such families.
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© 1983 Springer-Verlag
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Kettle, S.G. (1983). Classifying and enumerating some freely generated families of objects. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071524
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DOI: https://doi.org/10.1007/BFb0071524
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