更多关于精确慢速$k$ -Nim
More about Exact Slow $k$-Nim
摘要：
给定$n$堆代币和正整数$k \leq n$，游戏Nim $^1_{n, =k}$的精确慢$k$ -Nim如下进行。两名球员交替移动。在每一步中，一名玩家准确地选择$k$非空堆，并从每个堆中移除一个代币。轮到该走棋但没有走棋的玩家输（如果玩的是正常版本的游戏，如果玩的是悲惨版本的游戏则赢）。在Integers 20（2020）1-19中，Gurvich等人给出了Nim $^1_{4, =2}$的Sprague-Grundy函数的显式公式，包括其正常和misére版本。在这里，我们推广了这个结果，并获得了一个显式的P-位置的正常版本的Nim $^1_{5, =2}$和Nim $^1_{6, =2}$。
英文摘要：
Given $n$ piles of tokens and a positive integer $k \leq n$, the game Nim$^1_{n, =k}$ of exact slow $k$-Nim is played as follows. Two players move alternately. In each move, a player chooses exactly $k$ non-empty piles and removes one token from each of them. A player whose turn it is to move but has no move loses (if the normal version of the game is played, and wins if it is the misére version). In Integers 20 (2020) 1-19, Gurvich et al gave an explicit formula for the Sprague-Grundy function of Nim$^1_{4, =2}$, for both its normal and misére version. Here we extend this result and obtain an explicit formula for the P-positions of the normal version of Nim$^1_{5, =2}$ and Nim$^1_{6, =2}$.
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。
