ABSTRACT
A principle objective of combinatorial enumeration is to count the number of objects of a certain size in a given family. Lattice walks are an important family of combinatorial classes as they offer a straightforward encoding of many mathematical objects, yet remain easy to manipulate and to count. Rooted trees can represent structured information in a very natural way. Common set operations build combinatorial classes from old. Any operation must come equipped with a description of how the size is computed in the resulting set and a verification that the number of objects of any fixed given size is finite. Algebraic classes are well-studied in theoretical computer science. Languages that are specified by an algebraic grammar are known as context-free languages. A language is said to be an unambiguous if every element is derived in a unique way.
