Biased weak polyform achievement games

Ian Norris, Nandor Sieben

Research output: Contribution to journalArticle

Abstract

In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

Original languageEnglish (US)
Pages (from-to)147-172
Number of pages26
JournalDiscrete Mathematics and Theoretical Computer Science
Volume16
Issue number3
StatePublished - 2014

Fingerprint

Biased
Game
Polyominoes
Cell
Congruent
Strategy

Keywords

  • Biased achievement games
  • Priority strategy

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Biased weak polyform achievement games. / Norris, Ian; Sieben, Nandor.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 16, No. 3, 2014, p. 147-172.

Research output: Contribution to journalArticle

@article{33d6d076ad914d8ea6e1dcb012b0b1fc,
title = "Biased weak polyform achievement games",
abstract = "In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.",
keywords = "Biased achievement games, Priority strategy",
author = "Ian Norris and Nandor Sieben",
year = "2014",
language = "English (US)",
volume = "16",
pages = "147--172",
journal = "Discrete Mathematics and Theoretical Computer Science",
issn = "1365-8050",
publisher = "Maison de l'informatique et des mathematiques discretes",
number = "3",

}

TY - JOUR

T1 - Biased weak polyform achievement games

AU - Norris, Ian

AU - Sieben, Nandor

PY - 2014

Y1 - 2014

N2 - In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

AB - In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

KW - Biased achievement games

KW - Priority strategy

UR - http://www.scopus.com/inward/record.url?scp=84940338909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940338909&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 147

EP - 172

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

IS - 3

ER -