Avoidance (or misère) games are a type of positional games. Two players alternately claim points of a set $N$ (the `board' of the game). The game is determined by a family $L$ of subsets of $N$ and the following rule: The first player who claims every point of some set in $L$ loses the avoidance game. The game is called transitive if the group of all permutations of $N$ leaving $L$ invariant acts transitively on $N$. Johnson, Leader and Walters show that for a board size which is neither a prime number nor a power of two there are transitive avoidance games where the first player can force his win. For primes of size at least $17$, the corresponding problem remained open. We are going to close this gap and prove that for all primes $n$ of size at least $17$ there are also transitive avoidance games with board size $n$ where the first player can force his win.
@article{10_37236_10203,
author = {Matthias Gehnen and Eberhard Triesch},
title = {Transitive avoidance games on boards of odd size},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/10203},
zbl = {1475.91042},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10203/}
}
TY - JOUR
AU - Matthias Gehnen
AU - Eberhard Triesch
TI - Transitive avoidance games on boards of odd size
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10203/
DO - 10.37236/10203
ID - 10_37236_10203
ER -
%0 Journal Article
%A Matthias Gehnen
%A Eberhard Triesch
%T Transitive avoidance games on boards of odd size
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10203/
%R 10.37236/10203
%F 10_37236_10203
Matthias Gehnen; Eberhard Triesch. Transitive avoidance games on boards of odd size. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10203
