On the uniqueness conjecture for the maximum Stirling numbers of the second kind
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Fecha
2021-04-15
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Springer
Resumen
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).
Descripción
This 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/s00025-021-01393-7
Palabras clave
Stirling number of the second kind, uniqueness conjecture, multinomial law
Citación
Adell, J.A., Cárdenas-Morales, D. On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind. Results Math 76, 93 (2021)