English

Algorithms for lattice games

Combinatorics 2011-05-30 v1 Commutative Algebra

Abstract

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a given position is a winning position, and to find a move to a winning position, if not; and (ii) to decide whether two given positions are congruent, in the sense of mis\`ere quotient theory. The methods are based on the theory of short rational generating functions.

Keywords

Cite

@article{arxiv.1105.5413,
  title  = {Algorithms for lattice games},
  author = {Alan Guo and Ezra Miller},
  journal= {arXiv preprint arXiv:1105.5413},
  year   = {2011}
}

Comments

12 pages, no figures

R2 v1 2026-06-21T18:13:19.857Z