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# Recursive combinatorial species

The combinatorial species of rooted trees can be defined recursively via $A = X\cdot E(A)$, where $X$ denotes the singleton species and $E$ the set species. How can I make the following code work? The last command yields an error.

sage: X = species.SingletonSpecies()
sage: E = species.SetSpecies()
sage: A = CombinatorialSpecies()
sage: A.define(X*E(A))
sage: A.generating_series()

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## 1 Answer

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Like this (one has to tell the valuation now).

sage: X = species.SingletonSpecies()
sage: E = species.SetSpecies()
sage: A = CombinatorialSpecies(min=1)
sage: A.define(X*E(A))
sage: A
Combinatorial species with min=1
sage: A.generating_series()[0:4]
[0, 1, 1, 3/2]

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Asked: 2023-05-08 23:19:01 +0100

Seen: 60 times

Last updated: May 09 '23