Counting Lattice Points on Bargraphs of Catalan Words

Toufik Mansour; José L. Ramírez; Diana A. Toquica

doi:10.1007/s11786-021-00501-8

Counting Lattice Points on Bargraphs of Catalan Words

Toufik Mansour, José L. Ramírez, Diana A. Toquica

Department of Mathematics

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

Abstract

We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

Original language	English
Pages (from-to)	701-713
Number of pages	13
Journal	Mathematics in Computer Science
Volume	15
Issue number	4
DOIs	https://doi.org/10.1007/s11786-021-00501-8
State	Published - Dec 2021

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referees for carefully reading the paper and giving helpful comments and suggestions. The second author was partially supported by Universidad Nacional de Colombia, Project No. 46240.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.

Keywords

Catalan word
Generating function
Interior points
Vertex degree

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1007/s11786-021-00501-8

Cite this

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abstract = "We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.",

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note = "Funding Information: The authors would like to thank the anonymous referees for carefully reading the paper and giving helpful comments and suggestions. The second author was partially supported by Universidad Nacional de Colombia, Project No. 46240. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.",

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AU - Ramírez, José L.

AU - Toquica, Diana A.

N1 - Funding Information: The authors would like to thank the anonymous referees for carefully reading the paper and giving helpful comments and suggestions. The second author was partially supported by Universidad Nacional de Colombia, Project No. 46240. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.

PY - 2021/12

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N2 - We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

AB - We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

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KW - Vertex degree

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JO - Mathematics in Computer Science

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SN - 1661-8270

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Counting Lattice Points on Bargraphs of Catalan Words

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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