Wythoff partizan subtraction
type: Item
instance of: scholarly article
title: Wythoff partizan subtraction
zbMATH Open document ID: 1457.91115
author: Urban Larsson
author: Neil A. McKay
author: R. J. Nowakowski
author: Angela A. Siegel
published in: International Journal of Game Theory
publication date: 2018-10-04T00:00:00Z
review text: The authors study solution for a class of two-player subtraction games. Subtraction games are zero-sum games with the following structure: there is a finite set of heaps of counters, and the players take turns to choose a heap and decide how many counters to remove from it. Each player has a subtraction set, which specifies the allowable numbers of counters to remove that he can choose from. A player who has no allowable moves loses. The authors consider partizan games, meaning that the players have different subtraction sets. The topic of the paper is complementary subtraction games, where one player has a subtraction set A and the other player's subtraction set B is all the positive integers not in A. The focus specifically is on the case where A and B are taken from \textit{W. A. Wythoff}'s sequences [Nieuw Arch. Wiskd., II. Ser. 7, 199--202 (1906; JFM 37.0261.03)]. The authors characterize the winning positions for each player in such games, using properties of the Fibonacci sequence.
reviewed by: Thomas Wiseman
Mathematics Subject Classification ID: 91A46
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 6947135
zbMATH Keywords: combinatorial game theory
zbMATH Keywords: complementary subtraction
zbMATH Keywords: Fibonacci sequence
zbMATH Keywords: partizan subtraction game
zbMATH Keywords: reduced canonical form
zbMATH Keywords: Sturmian word
zbMATH Keywords: Wythoff's sequences
MaRDI profile type: Publication
full work available at URL: s00182-018-0613-2
OpenAlex ID: W2793367700
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DOI: 10.1007/S00182-018-0613-2
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description: scientific article; zbMATH DE number 6947135