論文の公開元へA Study on Combinatorial Games
概要
In this thesis, we study combinatorial games, in particular, a class of impartial games.
First, we study a combination (called the generalized cyclic Nimhoff) of the cyclic Nimhoff and subtraction games. We give the G-value of the game when all the G-value sequences of the component subtraction games have a common h-stair structure.
Next, we study a game (called Delete Nim) which requires the OR operation to calculate the G- values of its positions. In addition, the concept called 2-adic valuation, which is described in number theory, is utilized. This is very rare in analysis of impartial games, while the XOR operation is commonly used for calculations of the G-values. Therefore, the research is expected to expand the potential strategies for analysis of impartial games.
