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Corpus ID: 201111993

AN IDENTITY INVOLVING STIRLING NUMBERS OF BOTH KINDS AND ITS CONNECTION TO RIGHT-TO-LEFT MINIMA OF CERTAIN SET PARTITIONS

@inproceedings{Herscovici2019ANII,
title={AN IDENTITY INVOLVING STIRLING NUMBERS OF BOTH KINDS AND ITS CONNECTION TO RIGHT-TO-LEFT MINIMA OF CERTAIN SET PARTITIONS},
author={O. Herscovici and R. Pinsky},
year={2019}
}

For 1 ≤ k ≤ n, n ∈ N, let S(n, k) denote the Stirling numbers of the second kind and let s(n, k) = (−1)n−k|s(n, k)| denote the Stirling numbers of the first kind, where |s(n, k)| denote the unsigned Stirling numbers of the first kind. Extend the definitions to all n, k ∈ N by defining all of these Stirling numbers to be equal to zero if k > n. Let S = {S(n, k)} (respectively, s = {s(n, k)}, |s| = {|s(n, k)|}) denote the infinite matrix whose nk-th entry is S(n, k) (respectively s(n, k), |s(n, k… Expand