A circular Nim game is a two player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks, and taking at least one token from one or more of the $k$ stacks. The last player able to make a move wins. We prove results on the structure of the losing positions for small $n$ and $k$ and pose some open questions for further investigations.
@article{10_37236_2765,
author = {Matthieu Dufour and Silvia Heubach},
title = {Circular {Nim} games},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/2765},
zbl = {1266.91016},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2765/}
}
TY - JOUR
AU - Matthieu Dufour
AU - Silvia Heubach
TI - Circular Nim games
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2765/
DO - 10.37236/2765
ID - 10_37236_2765
ER -
%0 Journal Article
%A Matthieu Dufour
%A Silvia Heubach
%T Circular Nim games
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2765/
%R 10.37236/2765
%F 10_37236_2765
Matthieu Dufour; Silvia Heubach. Circular Nim games. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/2765
