Integer Compositions and Higher-Order Conjugation
Augustine O. Munagi
School of Mathematics
University of the Witwatersrand
Wits 2050, Johannesburg
We consider the classical MacMahon conjugation of compositions or ordered
partitions of positive integers. Using both algebraic and graphical
methods we provide a natural extension of the standard conjugation of a
composition to higher orders. The higher-order conjugates of a composition
are obtained by varying the increments used in standard conjugation
to turn strings of ones into larger summands and vice versa. It turns
out that every nontrivial composition has an integral conjugation order
beyond which it is not conjugable. We also discuss recursive conjugation
and provide enumeration formulas and combinatorial identities between
different classes of compositions.
Full version: pdf,
(Concerned with sequences
Received May 29 2018; revised versions received August 30 2018; August 31 2018.
Published in Journal of Integer Sequences, November 25 2018.
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