250109 VO Selected topics in combinatorics (2016W)

The Art of Bijections

(Non-trivial) bijections are one of the most beautiful things in
combinatorics, which can be extremely powerful and insightful.
In the best case, they provide one-picture proofs of surprising
identities and relations between seemingly totally different
objects.

In this course, I shall explain various classical and not-so-classical
bijections for paths, trees, combinatorial maps, set and integer partitions,
tilings, tableaux, etc., culminating in the "queen of all bijections",
the Robinson-Schensted-Knuth correspondence and its "relatives".

While explaining an individual bijection, I will use the opportunity to
tell more about the respective subject.

Nothing except basic combinatorial facts (generating functions) are required.

Open problems are plenty (but probably very difficult).