Impartial Achievement Games on Convex Geometries
Combinatorics
2021-04-20 v2
Abstract
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to move. We develop a structure theory for these games and use it to determine the nim number for several classes of convex geometries, including one-dimensional affine geometries, vertex geometries of trees, and games with a winning set consisting of extreme points.
Cite
@article{arxiv.2010.11319,
title = {Impartial Achievement Games on Convex Geometries},
author = {Stephanie McCoy and Nándor Sieben},
journal= {arXiv preprint arXiv:2010.11319},
year = {2021}
}