Queen reflections: a modification of Wythoff Nim

Fokkink, Robbert and Rust, Dan (2022). Queen reflections: a modification of Wythoff Nim. International Journal of Game Theory (Early Access).

DOI: https://doi.org/10.1007/s00182-022-00824-1

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.

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About

• Item ORO ID
• 82486
• Item Type
• Journal Item
• ISSN
• 1432-1270
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Visitor grant	040.11.700	Dutch Science Federation
  Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications	CRC1283	German Research Foundation

• Keywords
• Impartial Combinatorial Games; k-bonacci words; Integer Sequences
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2022 The Author(s)
• Depositing User
• Dan Rust