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Combinatorial species
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In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions. Examples of discrete structures are (finite) graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size.
Category theory provides a useful language for the concepts that arise here, but it is not necessary to understand categories before being able to work with species.
The category of species is equivalent to the category of symmetric sequences in finite sets.[1]
.Category theory provides a useful language for the concepts that arise here, but it is not necessary to understand categories before being able to work with species.
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