The linking-unlinking game
Copyright policy )The linking-unlinking game
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.
34 pages, 30 figures
- Elmira College United States
- Louisiana State University United States
- Louisiana State University System United States
- Louisiana State University United States
pseudodiagram, link, winning strategy, two-person game, rational link, two-player game, Mathematics - Geometric Topology, knot, FOS: Mathematics, Mathematics - Combinatorics, Combinatorial games, link shadow, splittable, Knot theory, Geometric Topology (math.GT), 91A46, 2-person games, unsplittable, link diagram, linking-unlinking game, 57M25, Combinatorics (math.CO), rational tangle, knot diagram
pseudodiagram, link, winning strategy, two-person game, rational link, two-player game, Mathematics - Geometric Topology, knot, FOS: Mathematics, Mathematics - Combinatorics, Combinatorial games, link shadow, splittable, Knot theory, Geometric Topology (math.GT), 91A46, 2-person games, unsplittable, link diagram, linking-unlinking game, 57M25, Combinatorics (math.CO), rational tangle, knot diagram
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