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Matching points in compositions and words

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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.

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Author information

Authors and Affiliations

  1. The John Knopfmacher Centre for Applicable Analysis and Number Theory School of Mathematics, University of the Witwatersrand, Private Bag 3 Wits, Johannesburg, 2050, South Africa

    Margaret Archibald, Aubrey Blecher & Arnold Knopfmacher

Authors
  1. Margaret Archibald
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  2. Aubrey Blecher
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  3. Arnold Knopfmacher
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Corresponding author

Correspondence to Aubrey Blecher.

Additional information

Communicated by Rahul Roy.

This material is based upon work supported by the National Research Foundation under grant numbers 89147, BLEC 018 and 81021 respectively.

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Archibald, M., Blecher, A. & Knopfmacher, A. Matching points in compositions and words. Indian J Pure Appl Math 54, 946–958 (2023). https://doi.org/10.1007/s13226-022-00312-y

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