Rock-Paper-Scissors Meets Borromean Rings

Chamberland, Marc; Herman, Eugene A.

doi:10.1007/s00283-014-9499-4

Cited by 9 publications

(4 citation statements)

References 1 publication

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“…The above result (and its proof) comes from Theorem 5.2 of [8]. In general, for a tournament of size p with score vector s = (s 1 , .…”

Section: Gamesmentioning

confidence: 96%

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Rock, Paper, Scissors, Etc -- Topics in the Theory of Regular Tournaments

Akin

2018

Preprint

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Following the extension of the classic Rock-Paper-Scissors game of size 3 to Rock-Paper-Scissors-Lizard-Spock of size 5, we consider further extensions to larger odd numbers. Such extensions are modeled by directed graphs called tournaments. The games we will consider are regular tournaments where each strategy beats and is beaten by exactly half of the alternatives. While the theory of tournaments has been well studied, these games, i.e. regular tournaments, have special properties which we consider here. In the process we introduce a number of constructions for such games.

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“…The above result (and its proof) comes from Theorem 5.2 of [8]. In general, for a tournament of size p with score vector s = (s 1 , .…”

Section: Gamesmentioning

confidence: 96%

“…In [8] Chamberland and Herman compute the number of isomorphism classes and associated automorphism groups for games of size 9, 11 and 13. In addition, they provide a beautiful geometric description of the three games of size 7.…”

Section: Games Of Size Ninementioning

confidence: 99%

Rock, Paper, Scissors, Etc -- Topics in the Theory of Regular Tournaments

Akin

2018

Preprint

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“…This game is conservative, essentially polyadic, strongly fair, and nondegenerate. r p s v l r r p r v r p p p s p l s r s s v s v v p v v l l r l s l l Variants of RPS with larger numbers of items appear in the literature as balanced tournaments [4]. Under this combinatorial definition it is well-established that only variants with an odd number of items may exist when the quantity of items to choose from is finite.…”

Section: R P S W R R P R W P P P S P S R S S W W W P W Wmentioning

confidence: 99%

Multiplayer Rock-Paper-Scissors

Aten

2019

Preprint

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“…In the context of Fig. 1(a), an edge's direction goes from the ring that is 'over' to the ring that is 'under' (Chamberland & Herman, 2015;O'Keeffe & Treacy, 2021). In some drawings of Borromean rings [Fig.…”

Section: Introductionmentioning

confidence: 99%

Periodic Borromean rings, rods and chains

O'Keeffe,

Treacy

2024

Acta Cryst Sect A

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This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families. A second isonemal 2-periodic family is identified, as is a unique 3-periodic Borromean assembly of equilateral triangles. Also reported is a notable 2-periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in place as a novel `quasi-Borromean' set of four repeating components.

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Rock-Paper-Scissors Meets Borromean Rings

Cited by 9 publications

References 1 publication

Rock, Paper, Scissors, Etc -- Topics in the Theory of Regular Tournaments

Rock, Paper, Scissors, Etc -- Topics in the Theory of Regular Tournaments

Multiplayer Rock-Paper-Scissors

Periodic Borromean rings, rods and chains

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