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

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.

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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。

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

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.