Pascal's formulas and vector fields

2022/10/21 by Chassaing, Philippe, Flin, Jules, Zevio, Alexis · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.11814

Abstract

We consider four examples of combinatorial triangles (T(n,k))_{0≤ k≤ n} (Pascal, Stirling of both types, Euler) : through saddle-point asymptotics, their Pascal's formulas define four vector fields, together with their field lines that turn out to be the conjectured limit of sample paths of four well known Markov chains. We prove this asymptotic behaviour in three of the four cases.

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