Matching points in compositions and words

Margaret Archibald (), Aubrey Blecher () and Arnold Knopfmacher ()
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Margaret Archibald: University of the Witwatersrand
Aubrey Blecher: University of the Witwatersrand
Arnold Knopfmacher: University of the Witwatersrand

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 946-958

Abstract: Abstract A matching point in compositions and words is an extension to these objects of the well-studied concept of fixed points in permutations. The equivalent of the derangement problem is solved here by providing a formula for the number of compositions of n having no matching points, and showing that the number of words with no matching points tends to zero as (the length of the word) n tends to infinity. We also find formulae for the average number of matching points in both words and compositions.

Keywords: Generating function; Fixed point; Derangement; Composition; Primary: 05A15; 05A16; Secondary: 05A05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00312-y

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