Real Zeros and Partitions without singleton blocks

Mikl\'os B\'ona , Istv\'an Mez\H{o}

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classification 🧮 math.CO math.PR

keywords blocksnumberpartitionsrealrootsapplyasymptoticbehavior

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We prove that the generating polynomials of partitions of an $n$-element set into non-singleton blocks, counted by the number of blocks, have real roots only and we study the asymptotic behavior of the leftmost roots. We apply this information to find the most likely number of blocks.

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Real Zeros and Partitions without singleton blocks

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