TL;DR
This paper introduces the Linking-Unlinking Game played on two-component link shadows, providing winning strategies for specific classes of links, thereby connecting combinatorial game theory with knot theory.
Contribution
It presents the Linking-Unlinking Game and derives winning strategies for all shadows of two-component rational tangle closures and a broad family of two-component links.
Findings
Winning strategies for all shadows of two-component rational tangle closures.
Winning strategies for a large family of general two-component link shadows.
Establishment of a new combinatorial game framework in knot theory.
Abstract
Combinatorial two-player games have recently been applied to knot theory. Examples of this include the Knotting-Unknotting Game and the Region Unknotting Game, both of which are played on knot shadows. These are turn-based games played by two players, where each player has a separate goal to achieve in order to win the game. In this paper, we introduce the Linking-Unlinking Game which is played on two-component link shadows. We then present winning strategies for the Linking-Unlinking Game played on all shadows of two-component rational tangle closures and played on a large family of general two-component link shadows.
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