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

Abstract : 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.
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Journal articles
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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, November 17, 2022 - 5:28:16 PM
Last modification on : Tuesday, November 22, 2022 - 3:37:45 AM

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### Citation

Daniel Gourion. An upper bound for the number of chess diagrams without promotion. International Computer Games Association Journal, 2022, 44 (2), pp.44-55. ⟨10.3233/ICG-220210⟩. ⟨hal-03483904v2⟩

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