A.S. Fraenkel introduced a new $(s,t)$-Wythoff's game which is a generalization of both Wythoff's game and $a$-Wythoff's game. Four new models of a restricted version of $(s,t)$-Wythoff's game, Odd-Odd $(s,t)$-Wythoff's Game, Even-Even $(s,t)$-Wythoff's Game, Odd-Even $(s,t)$-Wythoff's Game and Even-Odd $(s,t)$-Wythoff's Game, are investigated. Under normal or misère play conventions, all $P$-positions of these four models are given for arbitrary integers $s,t\geq 1$. For Even-Even $(s,t)$-Wythoff's Game, the structure of $P$-positions is given by recursive characterizations in terms of the mex function. For other models, the structures of $P$-positions are of algebraic form, which permit us to decide in polynomial time whether or not a given game position $(a,b)$ is a $P$-position.
@article{10_37236_2963,
author = {Wen An Liu and Haiyan Li},
title = {General restriction of {\((s,t)\)-Wythoff's} game},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/2963},
zbl = {1305.91053},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2963/}
}
TY - JOUR
AU - Wen An Liu
AU - Haiyan Li
TI - General restriction of \((s,t)\)-Wythoff's game
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2963/
DO - 10.37236/2963
ID - 10_37236_2963
ER -
%0 Journal Article
%A Wen An Liu
%A Haiyan Li
%T General restriction of \((s,t)\)-Wythoff's game
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2963/
%R 10.37236/2963
%F 10_37236_2963
Wen An Liu; Haiyan Li. General restriction of \((s,t)\)-Wythoff's game. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/2963
