# An upper bound for the number of chess diagrams without promotion

Abstract : The number of legal chess diagrams without promotion is bounded from above by $2 \times 10^{40}$. This number is 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 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 structure, leading to a method for bounding pawn positions with any number of men on the board.
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Preprints, Working Papers, ...
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https://hal-univ-avignon.archives-ouvertes.fr/hal-03483904
Contributor : Daniel Gourion Connect in order to contact the contributor
Submitted on : Thursday, December 16, 2021 - 4:49:07 PM
Last modification on : Saturday, December 18, 2021 - 3:26:36 AM

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preprint1.pdf
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### Identifiers

• HAL Id : hal-03483904, version 1

### Citation

Daniel Gourion. An upper bound for the number of chess diagrams without promotion. 2021. ⟨hal-03483904⟩

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