Counting Nonattacking Chess Piece Placements: Bishops and Anassas
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912765943218176 |
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| author | Santos, E. G. |
| author_facet | Santos, E. G. |
| contents | We derive recurrences and closed-form expressions for counting nonattacking placements of two types of chess pieces with unbounded straight-line moves, namely the bishop (two diagonal moves) and the anassa (one horizontal or vertical move and one diagonal move), placed on a standard square chessboard. Additionally, we obtain explicit expressions for the corresponding quasi-polynomial coefficients. The recurrences are derived by analyzing how nonattacking configurations attack a specific subset of board squares, employing a bijective argument to establish the relations. The main results are simplifications of known expressions for the bishop and a general counting formula for the anassa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting Nonattacking Chess Piece Placements: Bishops and Anassas Santos, E. G. Combinatorics 05A15, 00A08 We derive recurrences and closed-form expressions for counting nonattacking placements of two types of chess pieces with unbounded straight-line moves, namely the bishop (two diagonal moves) and the anassa (one horizontal or vertical move and one diagonal move), placed on a standard square chessboard. Additionally, we obtain explicit expressions for the corresponding quasi-polynomial coefficients. The recurrences are derived by analyzing how nonattacking configurations attack a specific subset of board squares, employing a bijective argument to establish the relations. The main results are simplifications of known expressions for the bishop and a general counting formula for the anassa. |
| title | Counting Nonattacking Chess Piece Placements: Bishops and Anassas |
| topic | Combinatorics 05A15, 00A08 |
| url | https://arxiv.org/abs/2411.16492 |