Sprague-Grundy values of the \(\mathcal{R}\)-Wythoff game
The electronic journal of combinatorics, Tome 22 (2015) no. 2
We examine the Sprague-Grundy values of the game of $\mathcal{R}$-Wythoff, a restriction of Wythoff's game introduced by Ho, where each move is either to remove a positive number of tokens from the larger pile or to remove the same number of tokens from both piles. Ho showed that the $P$-positions of $\mathcal{R}$-Wythoff agree with those of Wythoff's game, and found all positions of Sprague-Grundy value $1$. We describe all the positions of Sprague-Grundy value $2$ and $3$, and also conjecture a general form of the positions of Sprague-Grundy value $g$.
DOI :
10.37236/4579
Classification :
91A46, 91A05
Mots-clés : combinatorial games, Sprague-Grundy values, Wythoff's game
Mots-clés : combinatorial games, Sprague-Grundy values, Wythoff's game
Affiliations des auteurs :
Albert Gu 1
@article{10_37236_4579,
author = {Albert Gu},
title = {Sprague-Grundy values of the {\(\mathcal{R}\)-Wythoff} game},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4579},
zbl = {1319.91051},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4579/}
}
Albert Gu. Sprague-Grundy values of the \(\mathcal{R}\)-Wythoff game. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4579
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