The Depth of Compositions

Aubrey Blecher; Charlotte Brennan; Arnold Knopfmacher; Toufik Mansour

doi:10.1007/s11786-019-00421-8

The Depth of Compositions

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	69-76
Number of pages	8
Journal	Mathematics in Computer Science
Volume	14
Issue number	1
DOIs	https://doi.org/10.1007/s11786-019-00421-8
State	Published - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Automaton
Composition
Generating function

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11786-019-00421-8

Cite this

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The Depth of Compositions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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