TY - JOUR
T1 - Queen reflections
T2 - a modification of Wythoff Nim
AU - Fokkink, Robbert
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Impartial combinatorial game
KW - Integer sequence
KW - k-Bonacci word
UR - http://www.scopus.com/inward/record.url?scp=85140192681&partnerID=8YFLogxK
U2 - 10.1007/s00182-022-00824-1
DO - 10.1007/s00182-022-00824-1
M3 - Article
AN - SCOPUS:85140192681
SN - 0020-7276
JO - International Journal of Game Theory
JF - International Journal of Game Theory
ER -