Counting $r\times s$ rectangles in (Catalan) words
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929340621520896 |
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| author | Fried, Sela Mansour, Toufik |
| author_facet | Fried, Sela Mansour, Toufik |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting $r\times s$ rectangles in (Catalan) words Fried, Sela Mansour, Toufik Combinatorics 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. |
| title | Counting $r\times s$ rectangles in (Catalan) words |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.06962 |