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The Depth of Compositions

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Abstract

In this paper we consider compositions of n as bargraphs. The depth of a cell inside this graphical representation is the minimum number of horizontal and/or vertical unit steps that are needed to exit to the outside. The depth of the composition is the maximum depth over all cells of the composition. We use finite automata to study the generating function for the number of compositions having a depth of at least r.

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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

    Aubrey Blecher, Charlotte Brennan & Arnold Knopfmacher

  2. Department of Mathematics, University of Haifa, 3498838, Haifa, Israel

    Toufik Mansour

Authors
  1. Aubrey Blecher
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  2. Charlotte Brennan
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  3. Arnold Knopfmacher
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  4. Toufik Mansour
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Correspondence to Charlotte Brennan.

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C. Brennan and A. Knopfmacher: This material is based upon work supported by the National Research Foundation under Grant No. 86329 and 81021 respectively.

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Blecher, A., Brennan, C., Knopfmacher, A. et al. The Depth of Compositions. Math.Comput.Sci. 14, 69–76 (2020). https://doi.org/10.1007/s11786-019-00421-8

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  • DOI: https://doi.org/10.1007/s11786-019-00421-8

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