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arXiv · 2405.06962

Counting $r\times s$ rectangles in (Catalan) words

Sela Fried·Toufik Mansour
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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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Sela Fried, Toufik Mansour. 2024-05-11. Counting $r\times s$ rectangles in (Catalan) words. https://arxiv.org/abs/2405.06962

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