Matrix products of binomial coefficients and unsigned Stirling numbers

2020/12/30 by Knežević, Marin, Krčadinac, Vedran, Relić, Lucija
#05A10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.15307

Abstract

We study sums of the form ∑_k=mⁿ a_nk b_km, where a_nk and b_km are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common features: combinatorial interpretations, Pascal-like recurrences, inverse relations with their signed versions, and interpretations as coefficients of change between polynomial bases.

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