Encyclopedia > Combinatorial species

  Article Content

Combinatorial species

(This article is about a concept in combinatorial mathematics. There is also an article on the concept of species used in biology.)

The class of all finite sets, along with the class of all bijections from one to another, is a category. A combinatorial species is a covariant functor from that category into itself.

For example, the "species of permutations" maps each finite set A to the set of all permutations of A, and each bijection from A to another set B naturally induces a bijection from the set of all permutations of A to the set of all permutations of B. Similarly, the "species of partitions" can be defined by assigning to each finite set the set of all its partitions, and the "power set species" assigns to each finite set its power set.

Need to explain how to add, multiply, compose, and differentiate combinatorial species.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Reformed churches

... protestants were called Huguenots. The Reformed Church of France survived under persecution from 1559 until the Edict of Nantes (1598), the effect of which was to ...

 
 
 
This page was created in 22.6 ms