Vol. 12, No. 7, 2019

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The linking-unlinking game

Adam Giambrone and Jake Murphy

Vol. 12 (2019), No. 7, 1109–1141
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.

Keywords
knot, knot diagram, link, link diagram, linking-unlinking game, pseudodiagram, rational link, rational tangle, splittable, two-player game, unsplittable, winning strategy
Mathematical Subject Classification 2010
Primary: 57M25, 91A46
Milestones
Received: 30 July 2018
Revised: 17 May 2019
Accepted: 11 June 2019
Published: 12 October 2019

Communicated by Kenneth S. Berenhaut
Authors
Adam Giambrone
Elmira College
Elmira, NY
United States
Jake Murphy
Louisiana State University
Baton Rouge, LA
United States