STATISTICS ON BARGRAPHS OF CATALAN WORDS

David Callan; Toufik Mansour; José L. Ramírez

doi:10.25596/jalc-2021-177

STATISTICS ON BARGRAPHS OF CATALAN WORDS

David Callan, Toufik Mansour, José L. Ramírez

Department of Mathematics

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

Abstract

Catalan words are a particular case of growth-restricted words. Here we give the bivariate generating function for bargraphs associated to Catalan words according to the semiperimeter and area statistics. Exact formulas to count Catalan bargraphs according to the two statistics are also found. We show a connection to the Narayana numbers. Finally, we give similar results for the exterior corner statistic.

Original language	English
Pages (from-to)	177-196
Number of pages	20
Journal	Journal of Automata, Languages and Combinatorics
Volume	26
Issue number	3-4
DOIs	https://doi.org/10.25596/jalc-2021-177
State	Published - 2021

Bibliographical note

Publisher Copyright:
© Institut für Informatik · Justus-Liebig-Universität Giessen.

Keywords

Catalan word
area
external corners
generating function
semiperimeter

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.25596/jalc-2021-177

Cite this

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abstract = "Catalan words are a particular case of growth-restricted words. Here we give the bivariate generating function for bargraphs associated to Catalan words according to the semiperimeter and area statistics. Exact formulas to count Catalan bargraphs according to the two statistics are also found. We show a connection to the Narayana numbers. Finally, we give similar results for the exterior corner statistic.",

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language = "English",

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AU - Callan, David

AU - Mansour, Toufik

AU - Ramírez, José L.

N1 - Publisher Copyright: © Institut für Informatik · Justus-Liebig-Universität Giessen.

PY - 2021

Y1 - 2021

N2 - Catalan words are a particular case of growth-restricted words. Here we give the bivariate generating function for bargraphs associated to Catalan words according to the semiperimeter and area statistics. Exact formulas to count Catalan bargraphs according to the two statistics are also found. We show a connection to the Narayana numbers. Finally, we give similar results for the exterior corner statistic.

AB - Catalan words are a particular case of growth-restricted words. Here we give the bivariate generating function for bargraphs associated to Catalan words according to the semiperimeter and area statistics. Exact formulas to count Catalan bargraphs according to the two statistics are also found. We show a connection to the Narayana numbers. Finally, we give similar results for the exterior corner statistic.

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KW - area

KW - external corners

KW - generating function

KW - semiperimeter

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JO - Journal of Automata, Languages and Combinatorics

JF - Journal of Automata, Languages and Combinatorics

IS - 3-4

ER -

STATISTICS ON BARGRAPHS OF CATALAN WORDS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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