Perfect Compositions of Numbers
Augustine O. Munagi
School of Mathematics
University of the Witwatersrand
Wits 2050, Johannesburg
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.
Full version: pdf,
(Concerned with sequences
Received December 30 2019; revised version received May 6 2020.
Published in Journal of Integer Sequences,
May 7 2020.
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