$m$-模威佐夫博弈
$m$-Modular Wythoff
AI总结：
本文提出$m$-模威佐夫博弈，将两堆取子数相等的条件弱化为模$m$等价，并证明其P位置是原始威佐夫博弈P位置的有限子集。
摘要：
我们引入威佐夫博弈的一个变体，称之为$m$-模威佐夫博弈。在原始威佐夫博弈中，玩家可以从一堆中取走正数数量的筹码，或者可以从两堆中各取走正数数量的筹码，前提是从第一堆取走的筹码数等于从第二堆取走的筹码数。在我们的变体中，我们将这一相等条件弱化为模$m$等价。我们将$m$-模变体的P位置刻画为原始威佐夫博弈已知P位置的一个有限子集。
英文摘要：
We introduce a variant of Wythoff's Game that we call $m$-Modular Wythoff's Game. In the original Wythoff's Game, players can take a positive number of tokens from one pile, or they can take a positive number of tokens from both piles if the number of tokens they take from the first pile is equal to the number of tokens they take from the second. In our variant, we weaken this equality condition to one of equivalence modulo $m$. We characterize the P-positions of our $m$-Modular variant as a finite subset of the P-positions of the known P-positions of the original Wythoff's Game.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
