An upper bound for the number of chess diagrams without promotion - Avignon Université Access content directly
Journal Articles International Computer Games Association Journal Year : 2022

An upper bound for the number of chess diagrams without promotion

Daniel Gourion

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.
Fichier principal
Vignette du fichier
postprint.pdf (239.87 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

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⟩
392 View
830 Download

Altmetric

Share

Gmail Facebook X LinkedIn More