有限群生成成就博弈的nim值谱

生成有限群的无偏达成与回避博弈

Impartial achievement and avoidance games for generating finite groups

研究生成有限群的两个无偏博弈，利用结构图工具确定阿贝尔群和二面体群的nim数，并提出基于计算的猜想。

Impartial achievement games for generating generalized dihedral groups

We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for generalized dihedral groups, which are of the form $\operatorname{Dih}(A)= \mathbb{Z}_2 \ltimes A$ for a finite abelian group $A$.

生成幂零群的公平博弈

Impartial achievement games for generating nilpotent groups

研究Anderson和Harary提出的公平博弈，确定形如$T \ imes H$（$T$为$2$-群，$H$为奇数阶群）的有限群的nim数，涵盖所有幂零群和阿贝尔群。

生成对称群与交错群的公正回避与达成博弈

Impartial avoidance and achievement games for generating symmetric and alternating groups

本研究分析对称群与交错群上的两种公正博弈，通过计算尼姆数确定其胜负结果，为有限群生成集博弈提供了理论判定。

有限群的公正回避博弈

Impartial avoidance games for generating finite groups

研究有限群上的公正回避博弈，通过极大子群判定nim数，并应用于幂零、零星及对称群。

两个有限群上的无偏博弈

Impartial games on two finite Groups

本文研究Anderson和Harary引入的无偏成就博弈和无偏避免博弈，利用极大子群准则分析了Frobenius群和所有子群均为阿贝尔群的非阿贝尔群上的博弈。