Mathematical Analysis of the King Wen Permutation in I Ching Hexagram Orderings
By
gezhengwen
Even the toaster can't save this one.
Summary
The article presents a mathematical analysis of the King Wen permutation, which maps between the two canonical orderings of the 64 I Ching hexagrams. The permutation's cycle decomposition reveals a pattern of [52, 10, 2] with zero fixed points, indicating that 81% of hexagrams are in one large orbit, suggesting the reordering is highly coupled rather than composed of small local swaps. This specific cycle type appears not to have been previously discussed in the literature.
Key quotes
· 3 pulledTreating the map between them as a permutation in S₆₄, its cycle decomposition yields [52, 10, 2] with zero fixed points (P≈0.37 for random permutations).
81% of hexagrams are in one orbit, meaning the reordering is highly coupled rather than a collection of small local swaps.
We have not found this cycle type discussed in the literature we surveyed.
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