On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind
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 multinom...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de Zaragoza |
| Repositorio: | Zaguán. Repositorio Digital de la Universidad de Zaragoza |
| OAI Identifier: | oai:zaguan.unizar.es:118138 |
| Acesso em linha: | http://zaguan.unizar.es/record/118138 |
| Access Level: | acceso abierto |
| Resumo: | 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). © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG. |
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