Indecomposable combinatorial games

IF 0.9 2区 数学 Q2 MATHEMATICS Journal of Combinatorial Theory Series A Pub Date : 2024-10-15 DOI:10.1016/j.jcta.2024.105964
Michael Fisher , Neil A. McKay , Rebecca Milley , Richard J. Nowakowski , Carlos P. Santos
{"title":"Indecomposable combinatorial games","authors":"Michael Fisher ,&nbsp;Neil A. McKay ,&nbsp;Rebecca Milley ,&nbsp;Richard J. Nowakowski ,&nbsp;Carlos P. Santos","doi":"10.1016/j.jcta.2024.105964","DOIUrl":null,"url":null,"abstract":"<div><div>In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If there are no such summands, then the form is indecomposable. The main contribution of this document is the characterization of the indecomposable nimbers and the characterization of the indecomposable numbers. More precisely, a nimber is indecomposable if and only if its size is a power of two, and a number is indecomposable if and only if its absolute value is less than or equal to one.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"209 ","pages":"Article 105964"},"PeriodicalIF":0.9000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524001031","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If there are no such summands, then the form is indecomposable. The main contribution of this document is the characterization of the indecomposable nimbers and the characterization of the indecomposable numbers. More precisely, a nimber is indecomposable if and only if its size is a power of two, and a number is indecomposable if and only if its absolute value is less than or equal to one.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
不可分解的组合博弈
在组合博弈论中,简短博弈形式是在允许两位棋手移动的所有位置上递归定义的。如果一个形式可以表示为两个生日较小的形式的析取和,那么这个形式就是可分解的。如果没有这样的和,那么这个棋形就是不可分解的。本文的主要贡献在于描述了不可分解数的特征和不可分解数的特征。更确切地说,当且仅当一个数的大小是 2 的幂时,它是不可分解的;当且仅当一个数的绝对值小于或等于 1 时,它是不可分解的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.90
自引率
9.10%
发文量
94
审稿时长
12 months
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
期刊最新文献
Dominance complexes, neighborhood complexes and combinatorial Alexander duals Upper bounds for the number of substructures in finite geometries from the container method The vector space generated by permutations of a trade or a design Editorial Board Some conjectures of Ballantine and Merca on truncated sums and the minimal excludant in congruences classes
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1