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

University of Haifa

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	American 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

Keywords

Catalan word
area
external corners
generating function
semiperimeter

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.25596/jalc-2021-177

Cite this

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title = "STATISTICS ON BARGRAPHS OF CATALAN WORDS",

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.",

keywords = "Catalan word, area, external corners, generating function, semiperimeter",

author = "David Callan and Toufik Mansour and Ram{\'i}rez, \{Jos{\'e} L.\}",

note = "Publisher Copyright: {\textcopyright} Institut f{\"u}r Informatik · Justus-Liebig-Universit{\"a}t Giessen.",

year = "2021",

doi = "10.25596/jalc-2021-177",

language = "American English",

volume = "26",

pages = "177--196",

journal = "Journal of Automata, Languages and Combinatorics",

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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.

KW - Catalan word

KW - area

KW - external corners

KW - generating function

KW - semiperimeter

UR - http://www.scopus.com/inward/record.url?scp=85153342038&partnerID=8YFLogxK

U2 - 10.25596/jalc-2021-177

DO - 10.25596/jalc-2021-177

M3 - Article

SN - 1430-189X

VL - 26

SP - 177

EP - 196

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

Keywords

All Science Journal Classification (ASJC) codes

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