Counting r×s rectangles in (Catalan) words

Sela Fried; Toufik Mansour

doi:10.1016/j.dam.2025.01.031

Counting r×s rectangles in (Catalan) words

Sela Fried, Toufik Mansour

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

Abstract

Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers r and s, this statistic counts the number of occurrences of a rectangle of size r×s in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of r×s rectangles and the generating function for their total number over all words. We also obtain the analog results for Catalan words.

Original language	English
Pages (from-to)	247-259
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	365
DOIs	https://doi.org/10.1016/j.dam.2025.01.031
State	Published - 15 Apr 2025
Externally published	Yes

Keywords

Bargraph
Catalan word
Chebyshev polynomial
Generating function
Word

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2025.01.031

Cite this

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title = "Counting r×s rectangles in (Catalan) words",

abstract = "Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers r and s, this statistic counts the number of occurrences of a rectangle of size r×s in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of r×s rectangles and the generating function for their total number over all words. We also obtain the analog results for Catalan words.",

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AU - Fried, Sela

AU - Mansour, Toufik

PY - 2025/4/15

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N2 - Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers r and s, this statistic counts the number of occurrences of a rectangle of size r×s in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of r×s rectangles and the generating function for their total number over all words. We also obtain the analog results for Catalan words.

AB - Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers r and s, this statistic counts the number of occurrences of a rectangle of size r×s in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of r×s rectangles and the generating function for their total number over all words. We also obtain the analog results for Catalan words.

KW - Bargraph

KW - Catalan word

KW - Chebyshev polynomial

KW - Generating function

KW - Word

UR - https://www.scopus.com/pages/publications/85216624058

U2 - 10.1016/j.dam.2025.01.031

DO - 10.1016/j.dam.2025.01.031

M3 - Article

AN - SCOPUS:85216624058

SN - 0166-218X

VL - 365

SP - 247

EP - 259

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Counting r×s rectangles in (Catalan) words

Abstract

Keywords

ASJC Scopus subject areas

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