Résumé : I will discuss a fairly new method for solving certain systems of functional equations arising in combinatorics. I will start by describing the work of Bernardi, Bousquet-Mélou and Raschel on enumerating walks with small steps in the quarter plane, then I will describe how I have applied this method more generally, in particular to counting certain walks by winding angle. In each case the solutions involve Jacobi theta functions.
[Slides.pdf] [vidéo]
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