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On the Periodicity of Chinese Sexagenary Indices

I have written a short note on the periodicity of Chinese sexagenary indices or bazi 八字, \(\mathbf{I} = (I_{\rm year}, I_{\rm month}, I_{\rm day}, I_{\rm hour})\), after reading a book by Hee, an accountant by training, on the same subject, many years ago. I was motivated primarily by a section of her book. In page 22, Hee wrote: . . . because of the numerous possible combinations, it takes 60 years for the same set of year pillars to repeat itself (by comparison, a set of month pillars repeats itself after just five years). Therefore, if you have a certain day and time, the set of four pillars will repeat itself in 60 years. However, since the same day may not appear in exactly the same month - and even if it is in the same month, the day may not be found in the same half month - it takes 240 years before the identical four pillars appear again. . . Basically, Hee's claims are as follows: When considered independently, the periodicity of the year-index, \(I_{\rm year}\), is…