The Depth of Compositions

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)69-76
Number of pages8
JournalMathematics in Computer Science
Issue number1
StatePublished - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.


  • Automaton
  • Composition
  • Generating function

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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