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Results tagged with combinatorial-game-theory
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user 75293
Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games
1
vote
Nim and the Sierpinski Gasket
Although the connection between Nim and the Sierpinski Gasket has not been explicitly proven (or I have not seen it), I would hesitate to believe that no one has thought of it before. The reason being …
- 1,129
3
votes
1
answer
335
views
Minimal Birthdays
In combinatorial game theory: The birthday of a game is defined recursively as 1 plus the maximal birthday of its options, with the zero game having birthday 0.
Suppose we define the quasi-birthday o …
- 1,129
5
votes
0
answers
304
views
Generalization of Sprague-Grundy Theorem
In my research on Combinatorial Game Theory, I used a certain theorem that is essentially a generalization of the Sprague-Grundy theorem. Because the result hinges too much on the work of others to be …
- 1,129
3
votes
0
answers
700
views
Nimbers and Surreal Numbers [closed]
I have been researching Combinatorial Game Theory. One common theme is the assignment of values to games in order to classify the game as a win for a specific player. One such way is class of surreal …
- 1,129
15
votes
3
answers
2k
views
Why does the bitxor function appear in Nim?
I am conducting research in Combinatorial Game Theory (CGT). Although I have done a considerable amount of reading, I do not completely understand why the bit-xor function also known as the nim-sum ap …
- 1,129