On partitions without small parts. (English) Zbl 1005.11049

The authors apply the saddle point method to the generating function of the partition function \(r(n,m)\), which counts the number of partitions of \(n\) into parts, each of which is at least \(m\). They obtain an asymptotic estimate which holds for large \(n\) and \(1\leq m\leq c_1n/ (\log n)^{c_2}\).


11P82 Analytic theory of partitions
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Online Encyclopedia of Integer Sequences:

Number of partitions of n that do not contain 1 as a part.


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