Black-White Cell Capacity in $k$-ary Words and Permutations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914029609418752 |
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| author | Fried, Sela |
| author_facet | Fried, Sela |
| contents | We introduce a new bargraph statistic that we call black-white cell capacity. It is obtained by coloring the cells of the bargraph in a chessboard style and recording the numbers of black and white cells contained in the bargraph. We study two word families under this statistic: $k$-ary words and permutations. We obtain the corresponding generating function, in the $k$-ary words case, and a closed-form formula for each $n$, in the permutations case. Of special interest are words containing an equal number of black and white cells, that we call bw-balanced. We obtain generating functions, closed-form formulas, and asymptotics in both cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Black-White Cell Capacity in $k$-ary Words and Permutations Fried, Sela Combinatorics We introduce a new bargraph statistic that we call black-white cell capacity. It is obtained by coloring the cells of the bargraph in a chessboard style and recording the numbers of black and white cells contained in the bargraph. We study two word families under this statistic: $k$-ary words and permutations. We obtain the corresponding generating function, in the $k$-ary words case, and a closed-form formula for each $n$, in the permutations case. Of special interest are words containing an equal number of black and white cells, that we call bw-balanced. We obtain generating functions, closed-form formulas, and asymptotics in both cases. |
| title | Black-White Cell Capacity in $k$-ary Words and Permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.07533 |