Adell, José A.Cárdenas-Morales, Daniel2024-09-092024-09-092021-04-15Adell, J.A., Cárdenas-Morales, D. On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind. Results Math 76, 93 (2021)1422-6383https://doi.org/10.1007/s00025-021-01393-7https://hdl.handle.net/10953/3182This version of the article was accepted for publication after peer review. It is subject to Springer Nature’s AM terms of use. It is not the Version of Record, available online at https://doi.org/10.1007/s00025-021-01393-7The 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).Stirling number of the second kinduniqueness conjecturemultinomial lawinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess