Speakers
- Eva-Maria Hainzl — École Polytechnique
Abstract
Discrete differential equations (DDEs), also known as catalytic equations, appear in the enumeration of several combinatorial classes, such as lattice walks, polyominoes, planar maps, parking trees and many more. Given a first order DDE with positive coefficients, we discuss its generic combinatorial interpretation in terms of non-negative Q-trees, which are trees where each vertex consists of a chain of blue, red and black pearls and the difference of blue and red pearls, called the excess, satisfies a non-negativity condition in each subtree. We study their asymptotic enumeration and limit laws of certain parameters using analytic combinatorics.
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