Advanced combinatorial analysis

The basic tools - combinations, arrangements and screens - were introduced and commented on in the previous booklet. Now we're going to introduce some more advanced ones, such as the notion of repetition, which will be studied at length.

Classical examples of applications of the entire combinatorial apparatus thus forged will then be proposed. The historical cases of households, anniversaries, parentheses, Fibonacci and Lucas numbers, not forgetting a few other well-felt examples from Geometry, will be treated in detail.

Finally, a general study of various developments, convergent or not, useful in future in-depth combinatorial calculations, will round off this second part with some little-known results.

The article "Combinatorial analysis" is the subject of several issues:

AF 200 Elementary combinatorial analysis

AF 201 Advanced combinatorial analysis

AF 202 In-depth combinatorial analysis

The subjects are not independent of each other.

Readers will need to refer back to the other issues often enough.

Please refer to the Bibliography.

A table of notations and abbreviations is given at the beginning of the booklet.