Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.1

Perfect Compositions of Numbers

Augustine O. Munagi
School of Mathematics
University of the Witwatersrand
Wits 2050, Johannesburg
South Africa


A perfect composition of a positive integer is one whose sequence of parts contains one composition of every smaller positive integer. We obtain explicit formulas based on the observation that perfect compositions are identical with certain restricted permutations of perfect partitions. We also consider n-color perfect compositions.

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(Concerned with sequences A001339 A002033 A064618 A074206 A165552 A330773 A330774.)

Received December 30 2019; revised version received May 6 2020. Published in Journal of Integer Sequences, May 7 2020.

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