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Species


A species of structures is a rule F which

1. Produces, for each finite set U, a finite set F[U],

2. Produces, for each bijection sigma:U->V, a function

 F[sigma]:F[U]->F[V].
(1)

The functions F[sigma] should further satisfy the following functorial properties:

1. For all bijections sigma:U->V and tau:V->W,

 F[tau degreessigma]=F[tau] degreesF[sigma],
(2)

2. For the identity map Id_(U):U->U,

 F[Id_(U)]=Id_(F[U]).
(3)

An element sigma in F[U] is called an F-structure on U (or a structure of species F on U). The function F[sigma] is called the transport of F-structures along sigma.


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References

Bergeron, F.; Labelle, G.; and Leroux, P. Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, p. 5, 1998.

Referenced on Wolfram|Alpha

Species

Cite this as:

Weisstein, Eric W. "Species." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Species.html

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