Rational and algebraic series in combinatorial enumeration

  title={Rational and algebraic series in combinatorial enumeration},
  author={Mireille Bousquet-M'elou},
Let A be a class of objects, equipped with an integer size such that for all n the number an of objects of size n is finite. We are interested in the case where the generating functionn antn is rational, or more generally algebraic. This property has a practical interest, since one can usually say a lot on the numbers an, but also a combinatorial one: the rational or algebraic nature of the generating function suggests that the objects have a (possibly hidden) structure, similar to the linear… 

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