Show HN: The King Wen Permutation: [52, 10, 2]

2026-03-23 | original

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Why This Matters

This discovery of the King Wen permutation's unique cycle structure offers new insights into the ancient Chinese text's organization, revealing complex mathematical patterns that were previously unrecognized. For the tech industry, it highlights the potential for uncovering hidden structures in data, inspiring innovative approaches in data analysis and algorithm design. For consumers, it underscores the enduring relevance of ancient knowledge and its unexpected intersections with modern technology.

Key Takeaways

The permutation reveals a complex cycle structure with no fixed points.
81% of hexagrams are contained within a single cycle, indicating a deep interconnectedness.
This mathematical insight is a novel finding that bridges ancient texts and modern data analysis.

The King Wen Permutation

A mathematical observation on a 3,000-year-old Chinese text

52 cycle | 10 cycle | 2 cycle

The 64 hexagrams of the I Ching have two canonical orderings: the binary natural order (0–63) and the King Wen sequence (~1000 BCE). Treating the map between them as a permutation in S₆₄, its cycle decomposition yields [52, 10, 2] with zero fixed points. 81% of hexagrams are locked in a single cycle. This structure has not been previously reported in the literature.

Explore topics: iching king wen permutation hexagrams s₆₄