论文标题
$ \ Mathcal {p} $ - $（2n+1）$的自我相似
Self-similarity of $\mathcal{P}$-positions of $(2n+1)$-dimensional Wythoff's game
论文作者
论文摘要
Wythoff作为经典组合游戏的游戏进行了很好的研究。在本文中，我们专注于$（2N+1）$ - 维索夫的游戏；那是Wythoff的游戏，拥有$（2N+1）$堆。我们表征他们的$ \ Mathcal {p} $ - 明确定位，并表明它们具有自相似结构。特别是，所有$ \ MATHCAL {P} $的集合的集合$ 3 $ - 维特Wythoff的游戏都会生成众所周知的分形集合--- Sierpinski Sponge。
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 $\mathcal{P}$-positions explicitly and show that they have self-similar structures. In particular, the set of all $\mathcal{P}$-positions of $3$-dimensional Wythoff's game generates the well-known fractal set---the Sierpinski sponge.
