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Algebraic enumeration is a subfield of enumeration that deals with finding exact formulas for the number of combinatorial objects of a given type, rather than estimating this number asymptotically. Methods of finding these formulas include generating functions and the solution of recurrence relations.[1]

References

Gessel, Ira M.; Stanley, Richard P. (1995), "Algebraic enumeration", Handbook of combinatorics, Vol. 1, 2, Amsterdam: Elsevier, pp. 1021–1061, MR 1373677.