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Mathematics in Computer Science

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13-11-2019

The Depth of Compositions

Authors: Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Published in: Mathematics in Computer Science | Issue 1/2020

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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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Title: The Depth of Compositions
Authors: Aubrey Blecher
Charlotte Brennan
Arnold Knopfmacher
Toufik Mansour
Publication date: 13-11-2019
Publisher: Springer International Publishing
Published in: Mathematics in Computer Science / Issue 1/2020
Print ISSN: 1661-8270
Electronic ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-019-00421-8

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