The Region Unknotting Game

Brown, Sarah M.; Cabrera, Francisco; Evans, Riley; Gibbs, Gianni; Henrich, Allison; Kreinbihl, James

doi:10.4169/math.mag.90.5.323

Cited by 5 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have enjoyed playing several two-player combinatorial games inspired by knot theory [2,3,4,5,6]. The focus of this paper, however, is a new type of knot game, called the KnotLink Game.…”

Section: Games Played On Knot and Link Diagramsmentioning

confidence: 99%

The KnotLink Game

Adams,

Henrich,

Stoll

2020

PUMP J. Undergrad. Res.

View full text Add to dashboard Cite

Recently, several new games have been introduced that can be played on knot and link diagrams. One of the first such games, played on knot diagrams, is called the Knotting-Unknotting Game. In this game, one player aims to create an unknot while their opponent tries to produce a nontrivial knot. The Linking-Unlinking Game is similar, but is played on link diagrams. In this game, one player's goal is to produce an unlink while the other player aims to create any nontrivial link. In our paper, we introduce a hybrid of these two games, called the KnotLink game, that can be played on either a knot or a link diagram. Moves and players' goals are similar to those of the previous two games, with one key difference that allows the game board to be transformed from a knot to a link or vice versa during game play. We describe this new game, provide a sample game, and prove several results regarding winning strategies for infinite families of rational knots and links.

show abstract

“…We have enjoyed playing several two-player combinatorial games inspired by knot theory [2,3,4,5,6]. The focus of this paper, however, is a new type of knot game, called the KnotLink Game.…”

Section: Games Played On Knot and Link Diagramsmentioning

confidence: 99%

The KnotLink Game

Adams,

Henrich,

Stoll

2020

PUMP J. Undergrad. Res.

View full text Add to dashboard Cite

show abstract

“…We introduce a new game, the Region Smoothing Swap Game, played on a game board derived from the connected shadow of a link diagram on a surface by smoothing at the diagram's crossings. This game can be viewed as a hybrid of the Link Smoothing Game, studied in [2], and the Region Unknotting Game, studied in [1].…”

mentioning

confidence: 99%

The Region Smoothing Swap Game

Henrich,

Johnson,

Ostroff

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We introduce a topological combinatorial game called the Region Smoothing Swap Game. The game is played on a game board derived from the connected shadow of a link diagram on a (possibly non-orientable) surface by smoothing at crossings. Moves in the game are performed on regions of the diagram and can switch the direction of certain crossings' smoothings. The players' goals relate to the connectedness of the diagram produced by game play.

show abstract

“…Untangle ( [4]), the Knotting-Unknotting Game ( [6], [8]), and the Region Unknotting Game ( [3]). The game Twist Untangle is played between two people on a nontrivial diagram of the unknot formed by iteratively twisting the unknotted circle.…”

mentioning

confidence: 99%

“…The key difference is that play now consists of resolving the set of crossings that are incident to a face of the knot shadow (or changing the crossing type of a crossing if it has already been resolved). For more details, see [3].…”

mentioning

confidence: 99%

The linking-unlinking game

Giambrone

Murphy

2019

Involve

View full text Add to dashboard Cite

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 twocomponent 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.

show abstract

The Region Unknotting Game

Cited by 5 publications

References 6 publications

The KnotLink Game

The KnotLink Game

The Region Smoothing Swap Game

The linking-unlinking game

Contact Info

Product

Resources

About