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ESTIMATE OF THE NUMBER OF RESTRICTED INTEGER-PARTITIONS

DOI: 10.2298/aadm0802222r

Keywords: Analytic combinatorics

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Abstract:

Using the saddle-point method an estimate is computed for the number $w_{ ext{m,N}}(n)$ of ordered $m$-partitions (compositions) of a positive integer $n$ under a constraint that the size of every part is at most $N$. The approximation error rate is $O(n^{-1/5}).

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