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Limits of Sums for Binomial and Eulerian Numbers and their Associated Distributions (1903.06317v1)
Published 15 Mar 2019 in math.CO, cs.DM, and math.PR
Abstract: We provide a unified, probabilistic approach using renewal theory to derive some novel limits of sums for the normalized binomial coefficients and for the normalized Eulerian numbers. We also investigate some corresponding results for their associated distributions -- the binomial distributions for the binomial coefficients and the Irwin-Hall distributions (uniform B-splines) for the Eulerian numbers.