An upper bound for the number of chess diagrams without promotion
Copyright policy )An upper bound for the number of chess diagrams without promotion
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.
- University of Avignon France
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)
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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