Domination Polynomial of the Rook Graph
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913259752259584 |
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| author | Mertens, Stephan |
| author_facet | Mertens, Stephan |
| contents | A placement of chess pieces on a chessboard is called dominating, if each free square of the chessboard is under attack by at least one piece. In this contribution we compute the number of dominating arrangements of $k$ rooks on an $n\times m$ chessboard. To this end we derive an expression for the corresponding generating function, the domination polynomial of the $n\times m$ rook graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Domination Polynomial of the Rook Graph Mertens, Stephan Combinatorics 05C69 (Primary) 05A15, 05C30, 11B83 (Secondary) A placement of chess pieces on a chessboard is called dominating, if each free square of the chessboard is under attack by at least one piece. In this contribution we compute the number of dominating arrangements of $k$ rooks on an $n\times m$ chessboard. To this end we derive an expression for the corresponding generating function, the domination polynomial of the $n\times m$ rook graph. |
| title | Domination Polynomial of the Rook Graph |
| topic | Combinatorics 05C69 (Primary) 05A15, 05C30, 11B83 (Secondary) |
| url | https://arxiv.org/abs/2401.00716 |