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.
Original language | English (US) |
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Article number | 101786 |
Journal | Computational Geometry: Theory and Applications |
Volume | 98 |
DOIs | |
State | Published - Oct 2021 |
Keywords
- Anti-matroid
- Convex closure
- Convex geometry
- Impartial game
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics