Some algebraic identity and its relations to Stirling numbers of the second kind

2022/10/28 by Lorek, Paweł
#11B73 #11B83 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.15966

Abstract

In this short note we provide some algebraic identity with a proof exploiting its probabilistic interpretation. We show several consequences of the identity, in particular we obtain a new representation of a Stirling number of second kind, S(n,d)=1\over d! ∑_1≤ j₁

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