SELF-SIMILARITY OF P-POSITIONS OF (2n+1)-DIMENSIONAL WYTHOFF'S GAME

摘要

Wythoff's game as a classic combinatorial game has been well studied. In this paper, we focus on (2n + 1)-dimensional Wythoff's game; that is the Wythoff's game with (2n + 1) heaps. We characterize their P-positions explicitly and show that they have self-similar structures. In particular, the set of all P-positions of 3-dimensional Wythoff's game generates the well-known fractal set - the Sierpinski sponge.

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