Queen reflections: a modification of Wythoff Nim

Robbert Fokkink () and Dan Rust ()
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Robbert Fokkink: Delft University of Technology
Dan Rust: The Open University

International Journal of Game Theory, 2024, vol. 53, issue 4, No 2, 1099-1117

Abstract: Abstract Wythoff Nim is a classical combinatorial game of queen moves on a chessboard. There are many ways to describe its P-positions (safe positions to move to). One way is to code them by the Fibonacci word 010010100100101..., which is the unique fixed point of the substitution of 0 by 01, and of 1 by 0. The coordinates of the n-th P-position are encoded by the location of the n-th zero and the n-th one in the Fibonacci word. We show that a minor modification of the rules of Wythoff Nim leads to a game with P-positions that are coded by 010010010010100100... This word can be derived by deleting all 2’s from the Tribonacci word, which is the unique fixed point of the substitution of 0 by 01, of 1 by 02, and of 2 by 0.

Keywords: Impartial combinatorial game; k-Bonacci word; Integer sequence; 91A46; 68R15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-022-00824-1

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