Enumerative Combinatorics 8: Species
نویسنده
چکیده
In this lecture I will discuss a very nice unifying principle for a number of topics in enumerative combinatorics, the theory of species, introduced by André Joyal in 1981. Species have been used in areas ranging from infinite permutation groups to statistical mechanics, and I can’t do more here than barely scratch the surface. Joyal gave a category-theoretic definition of species; I will take a more informal approach. There is a book on species, by Bergeron, Labelle and Leroux, entitled Combinatorial Species and Tree-Like Structures ; but I think that Joyal’s original paper in Advances in Mathematics is hard to beat.
منابع مشابه
An Introduction to q-Species
The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects constructed from vector spaces over finite fields. Examples of these objects include subspaces, flags of subspaces, direct sum decompositions, and linear maps ...
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