Pré-Publication, Document De Travail Année : 2021

An upper bound for the number of chess diagrams without promotion

Résumé

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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Dates et versions

hal-03483904 , version 1 (16-12-2021)
hal-03483904 , version 2 (17-11-2022)

Identifiants

  • HAL Id : hal-03483904 , version 1

Citer

Daniel Gourion. An upper bound for the number of chess diagrams without promotion. 2021. ⟨hal-03483904v1⟩
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