The Riordan group is an easy yet powerful tool for looking at a large
number of results in combinatorial enumeration. At the first level it
provides quick proofs for many binomial identities as well as a
systematic way to invert them. We will see how they arise naturally
when looking at the uplift principle as applied to classes of ordered
trees. We will also discuss some recent results including the Double
Riordan group, summer – winter trees, spoiled child trees, and will
mention a few open problems as well. The main tools involved are
generating functions, matrix multiplication, and elementary group
theory.
Seminar
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