A class of extensions of Restricted (s,t)-Wythoff’s game

Sanyang Liu; Haiyan Li

Open Mathematics (2017)

  • Volume: 15, Issue: 1, page 281-295
  • ISSN: 2391-5455

Abstract

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Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

How to cite

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Sanyang Liu, and Haiyan Li. "A class of extensions of Restricted (s,t)-Wythoff’s game." Open Mathematics 15.1 (2017): 281-295. <http://eudml.org/doc/288058>.

@article{SanyangLiu2017,
abstract = {Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.},
author = {Sanyang Liu, Haiyan Li},
journal = {Open Mathematics},
keywords = {Discrete mathematics; Combinatorial games; Wythoff’s game; Winning strategy; Computational complexity; discrete mathematics; combinatorial games; Wythoff's game; winning strategy; computational complexity},
language = {eng},
number = {1},
pages = {281-295},
title = {A class of extensions of Restricted (s,t)-Wythoff’s game},
url = {http://eudml.org/doc/288058},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Sanyang Liu
AU - Haiyan Li
TI - A class of extensions of Restricted (s,t)-Wythoff’s game
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 281
EP - 295
AB - Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.
LA - eng
KW - Discrete mathematics; Combinatorial games; Wythoff’s game; Winning strategy; Computational complexity; discrete mathematics; combinatorial games; Wythoff's game; winning strategy; computational complexity
UR - http://eudml.org/doc/288058
ER -

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