Fixed Points in Compositions and Words
M. Archibald, A. Blecher, and A. Knopfmacher
The John Knopfmacher Centre for
Applicable Analysis and Number Theory
University of the Witwatersrand
We study fixed points in compositions (ordered partitions) of integers
and words. A fixed point is a point with value i in position i. Using
generating functions and probabilistic arguments, we enumerate the
compositions and words with no fixed points and p fixed points and also
how many fixed points occur on average. We briefly discuss the average
maximum (respectively minimum) fixed point and the sum of sizes of fixed
points. Moreover we provide asymptotic results for the above parameters.
Full version: pdf,
(Concerned with sequences
Received March 23 2020; revised version received July 15 2020; October 28 2020.
Published in Journal of Integer Sequences,
November 7 2020.
Journal of Integer Sequences home page