横向波：一个公平的颜色传播游戏，灵感来自社会影响力和量子尼姆
Transverse Wave: an impartial color-propagation game inspired by Social Influence and Quantum Nim
摘要：
在本文中，我们研究了一个丰富多彩的，公平的组合游戏在一个二维网格，横向波。我们之所以被这个游戏所吸引，是因为它表面上很简单，对比起来却很棘手，而且与另外两个组合游戏有着内在的联系，一个是受社会影响的启发，另一个是受量子叠加的启发。更准确地说，我们表明，横波是在社会影响力启发的朋友圈和基于叠加的半量子尼姆的交叉点。横向波也与舍费尔的逻辑游戏避免真。除了分析横波的数学结构和计算复杂性之外，我们还提供了一个基于网络的游戏版本，可以在https://turing.plymouth.edu/~kgb1013/DB/combGames/transverseWave.html上玩。此外，我们制定了一个基本的网络影响启发游戏，称为人口影响，它同时概括了Node-Kyles和Demi-Quantum Nim（这反过来又包含Nim，Avoid True和Transverse Wave的特殊情况）。这些连接照亮格序，诱导的特殊情况下/泛化关系的数学游戏，基本的设计和比较分析的组合游戏。
英文摘要：
In this paper, we study a colorful, impartial combinatorial game played on a two-dimensional grid, Transverse Wave. We are drawn to this game because of its apparent simplicity, contrasting intractability, and intrinsic connection to two other combinatorial games, one inspired by social influence and another inspired by quantum superpositions. More precisely, we show that Transverse Wave is at the intersection of social-influence-inspired Friend Circle and superposition-based Demi-Quantum Nim. Transverse Wave is also connected with Schaefer's logic game Avoid True. In addition to analyzing the mathematical structures and computational complexity of Transverse Wave, we provide a web-based version of the game, playable at https://turing.plymouth.edu/~kgb1013/DB/combGames/transverseWave.html. Furthermore, we formulate a basic network-influence inspired game, called Demographic Influence, which simultaneously generalizes Node-Kyles and Demi-Quantum Nim (which in turn contains as special cases Nim, Avoid True, and Transverse Wave). These connections illuminate the lattice order, induced by special-case/generalization relationships over mathematical games, fundamental to both the design and comparative analyses of combinatorial games.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
