Donald Knuth introduced abstract CC systems to represent configurations of points in a plane with a given orientation (clockwise or counterclockwise) of all triples of points. We present efficient enumeration of all non-isomorphic CC systems with at most 12 points. Our algorithm is based on Faradžev-Read type enumeration, enhanced with the homomorphism principle and SAT solving, enabling us to enumerate more than $1.3\cdot {10}^{12}$ non-isomorphic CC systems with 12 points.

中文翻译：

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非同构CC系统的FaradževRead类型枚举

唐纳德·克努斯（Donald Knuth）引入了抽象CC系统，以表示平面中具有所有三重点的给定方向（顺时针或逆时针）的点的配置。我们提出了最多包含12个点的所有非同构CC系统的有效枚举。我们的算法基于Faradžev-Read类型的枚举，并通过同态原理和SAT求解得到增强，使我们能够枚举$1.3\cdot {10}^{12}$ 具有12点的非同构CC系统。