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Matching points in compositions and words

Author

Listed:
  • Margaret Archibald

    (University of the Witwatersrand)

  • Aubrey Blecher

    (University of the Witwatersrand)

  • Arnold Knopfmacher

    (University of the Witwatersrand)

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.

Suggested Citation

  • Margaret Archibald & Aubrey Blecher & Arnold Knopfmacher, 2023. "Matching points in compositions and words," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(3), pages 946-958, September.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:3:d:10.1007_s13226-022-00312-y
    DOI: 10.1007/s13226-022-00312-y
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