Evènement pour le groupe Combinatoire Énumérative et Algébrique

Date 2014-05-26  11:00-12:00
TitreAsymptotic Lattice Path Enumeration Using Diagonals 
RésuméCombining the kernel method with multivariate generating function analysis, we determine general formulas for the dominant asymptotics of counting sequences of walks restricted to the first orthant. The step sets under consideration are symmetric with respect to each axis, which is a strong condition, however the resulting formulas are very straightforward. The exponential growth of each model is given by the number of steps, while the sub-exponential growth depends only on the dimension of the underlying lattice and the number of steps moving forward in each coordinate. These expressions are derived by analyzing the singular variety of a multivariate rational function whose diagonal counts the lattice paths in question.  
OrateurSteve Melczer 
UrlSimon Fraser University, Vancouver, Canada 

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