Counting r×s rectangles in (Catalan) words

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-02-03 DOI:10.1016/j.dam.2025.01.031

Sela Fried , Toufik Mansour

引用次数: 0

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 \times s

in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of

r \times 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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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.