Please use this identifier to cite or link to this item: https://hdl.handle.net/10953/3182
Title: On the uniqueness conjecture for the maximum Stirling numbers of the second kind
Authors: Adell, José A.
Cárdenas-Morales, Daniel
Abstract: The Stirling numbers of the second kind S(n,k) satisfy S(n,0) < · · · < S(n,kn) ≥ S(n,kn+1) > · · · > S(n,n). A long standing conjecture asserts that there exists no n ≥ 3 such that S(n,kn) = S(n,kn +1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that S(n,kn)> S(n,kn+1).
Keywords: Stirling number of the second kind
uniqueness conjecture
multinomial law
Issue Date: 15-Apr-2021
metadata.dc.description.sponsorship: This work is partially supported by Research Project PGC2018-097621-B-I00. The second author is also supported by Junta de Andaluc´ıa Research Group FQM-0178.
Publisher: Springer
Citation: Adell, J.A., Cárdenas-Morales, D. On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind. Results Math 76, 93 (2021)
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