Editing Combinatorial class (section)

==Analytic combinatorics==
The theory of [[combinatorial species]] and its extension to [[analytic combinatorics]] provide a language for describing many important combinatorial classes, constructing new classes from combinations of previously defined ones, and automatically deriving their counting sequences.<ref name="ac"/> For example, two combinatorial classes may be combined by [[disjoint union]], or by a [[Cartesian product]] construction in which the objects are ordered pairs of one object from each of two classes, and the size function is the sum of the sizes of each object in the pair. These operations respectively form the addition and multiplication operations of a [[semiring]] on the family of (isomorphism equivalence classes of) combinatorial classes, in which the zero object is the empty combinatorial class, and the unit is the class whose only object is the [[empty set]].<ref>{{citation|title=Algebraic Cryptanalysis|first=Gregory V.|last=Bard|publisher=Springer|year=2009|isbn=9780387887579|at=Section 4.2.1, "Combinatorial Classes", ff., pp. 30–34|url=https://books.google.com/books?id=kjbp0mgu3IAC&pg=PA30}}.</ref>