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An upper bound for the number of chess diagrams without promotion

Name: An upper bound for the number of chess diagrams without promotion
Creator: Gourion, Daniel
Keywords: FOS: Computer and information sciences, chess, 05 social sciences, state space, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], Shannon’s number, Computer Science - Computer Science and Game Theory, 0502 economics and business, [INFO.INFO-GT] Computer Science [cs]/Computer Science and Game Theory [cs.GT]

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Oct 2022Embargo end date: 01 Jan 2021Publisher:SAGE PublicationsJournal:ICGA Journal, volume 44, pages 44-55 (issn: 1389-6911, eissn: 2468-2438,

Authors: Gourion, Daniel;

doi: 10.3233/icg-220210 , 10.48550/arxiv.2112.09386

arXiv: http://arxiv.org/abs/2112.09386

An upper bound for the number of chess diagrams without promotion

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Abstract

In 2015, Steinerberger showed that the number of legal chess diagrams without promotion is bounded from above by 2 × 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 × 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.

Related Organizations

University of Avignon
France

Keywords

FOS: Computer and information sciences, chess, state space, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], Shannon’s number, Computer Science - Computer Science and Game Theory, [INFO.INFO-GT] Computer Science [cs]/Computer Science and Game Theory [cs.GT], FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Computer Science and Game Theory (cs.GT)

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Fields of Science

social sciences

economics and business

Fields of Science

social sciences

economics and business

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