2011/07/13 by W. Wesley Johnson, Johnson, William
Computer Science · Mathematics · #91A44 #Artificial Intelligence in Games #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1107.2635
openalex publication_date 2011/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. Once the knot is fully resolved, the winner is decided by whether the knot is equivalent to the unknot. In this paper we determine which player wins under perfect play in the initial positions (knot shadows) that are guaranteed to produce rational knots or sums of rational knots. This is accomplished in part by an analysis of the effects of pseudo Reidemeister moves on positions, and a computer verification of some cases.