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Random Set Partitions
Journal article   Peer reviewed

Random Set Partitions

SIAM journal on discrete mathematics, v 7(3), pp 419-436
01 May 1994

Abstract

Approximation
For random partitions of $[ n ]$, let $L_n $ and $R_n $, respectively, denote the maximum block size and its multiplicity. The average multiplicity is $E( R_n ) = H( \{ m_n \} ) + o( 1 )$ as $n \to \infty $, where $H$ is an explicitly given analytic function and $\{ m_n \}$ is the fractional part of a certain implicitly defined root. The cumulative distribution function of $L_n $ also depends on $\{ m_n \}$. The sequence $\langle \{ m_n\}\rangle^{\infty}_{n=1}$ is dense in (0, 1). This establishes both the nonexistence of a limit distribution for $L_n $ and the nonexistence of a limiting value for $E( R_n )$.

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Mathematics
Mathematics, Applied
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