Poset positional games

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-02-25 DOI:10.1016/j.disc.2025.114455

Guillaume Bagan , Eric Duchêne , Florian Galliot , Valentin Gledel , Mirjana Mikalački , Nacim Oijid , Aline Parreau , Miloš Stojaković

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引用次数: 0

Abstract

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an additional structure – a poset on the elements of the board. Throughout the game play, based on this poset and the set of the board elements that are claimed up to that point, we reduce the set of available moves for the player whose turn it is – an element of the board can only be claimed if all the smaller elements in the poset are already claimed.

We proceed to analyze these games in more detail, with a prime focus on the most studied convention, the Maker-Breaker games. First we build a general framework around poset positional games. Then, we perform a comprehensive study of the complexity of determining the game outcome, conditioned on the structure of the family of winning sets on the one side and the structure of the poset on the other.

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偏置位置对策

我们提出了一种一般化的位置游戏，补充了一种限制顺序的方法，在这个顺序中，棋盘上的元素可以被主张。我们将介绍偏置位置游戏，这是一种带有附加结构的位置游戏——棋盘元素上的偏置。在整个游戏过程中，基于这个偏序集和到目前为止已被占用的棋盘元素集，我们减少轮到玩家的可用移动集——只有在偏序集中所有较小的元素都已被占用的情况下，棋盘上的一个元素才能被占用。接下来，我们将更详细地分析这些游戏，主要关注研究最多的惯例，即Maker-Breaker游戏。首先，我们围绕偏置位置游戏构建一个一般框架。然后，我们对决定游戏结果的复杂性进行了全面的研究，这取决于一方获胜集族的结构和另一方偏序集的结构。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.