Rules of succession among tuples
This is an attempt to define the minimal set of rules of succession for all tuples: even-odd pairs (PP), even triplets (ET) and 5-tuples (5T).
To do so, larger tuples are decomposed in smaller ones and singletons;
- An even triplet is made of a pair and an even singleton.
- An odd triplet is made of an odd singleton and a pair.
- A 5-tuple is made of a pair and an even triplet.
Each number is identify as follows: XXi.j, where XX is the type of tuples, i the position of the type of tuple upwards from a merge and j the position of the number in the tuple.
The figure below is based on a real case, in which numbers are replace by their identity. It contains three 5-tuples in a row to show the robustness of the rules. Note that tuples can be of more than one type (and color), due to decomposition.
Posted Apr 16, 2025, 5:14 AM UTC
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