An upper bound for the number of chess diagrams without promotion
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913652382105600 |
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| author | Gourion, Daniel |
| author_facet | Gourion, Daniel |
| contents | In 2015, Steinerberger showed that the number of legal chess diagrams without promotion is bounded from above by $2\times 10^{40}$. This number was obtained by restricting both bishops and pawns position and by a precise bound when no chessman has been captured. We improve this estimate and show that the number of legal diagrams is less than $4\times 10^{37}$. To achieve this, we define a graph on the set of diagrams and a notion of class of pawn arrangements, leading to a method for bounding pawn positions with any number of men on the board. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_09386 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An upper bound for the number of chess diagrams without promotion Gourion, Daniel Computer Science and Game Theory Combinatorics In 2015, Steinerberger showed that the number of legal chess diagrams without promotion is bounded from above by $2\times 10^{40}$. This number was obtained by restricting both bishops and pawns position and by a precise bound when no chessman has been captured. We improve this estimate and show that the number of legal diagrams is less than $4\times 10^{37}$. To achieve this, we define a graph on the set of diagrams and a notion of class of pawn arrangements, leading to a method for bounding pawn positions with any number of men on the board. |
| title | An upper bound for the number of chess diagrams without promotion |
| topic | Computer Science and Game Theory Combinatorics |
| url | https://arxiv.org/abs/2112.09386 |