Impartial achievement games on convex geometries

Stephanie McCoy, Nándor Sieben

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Article number101786
JournalComputational Geometry: Theory and Applications
Volume98
DOIs
StatePublished - 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

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