On 8-Colors Combinatorics and [ Quasi 24-Symmetry ]

by Frank C. Fung ( 1st published in March, 2011. )

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Section XXXV - The Effects of variations in the [ Read-Off Orders ]

Summary for the Section :

• In this Section , we shall be looking at the effects of varying the [ Read-Off Orders ] ,
  • while sticking with the [ Fu-Hei Scheme of Fixed-Positions ] .

  And for our discussions in the Section :

  • we shall use the { 5,040 [ Read-Off Orders ] with Fixed-Position [ FP-1 ] as the lead-off }
    • as our global set for the [ Read-Off Orders ] .

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Setting up the Question properly :

• Let us recall that the { Reduced Set of 5,040 [ 8-Colors Configurations ] } is made-up-of 5,040 distinct-and-different configurations .

  Thus , when we do the conversion to the [ 8-colors sequences ] , using :

  • the [ Fu-Hei Scheme of Fixed-Positions ] and any [ Read-Off Order ] ;
    • we do in fact get back 5,040 distinct-and-different [ 8-colors sequences ] , regardless .

• Since we have separated the 5,040 configurations into 210 physical [ sets-of-24 ] in the last Section ,
  • the question we have here is :
    • how will the corresponding 210 [ sets-of-24 8-colors-sequences ] behave ,
      • when we apply different [ Read-Off Orders ] to the 210 physical [ sets-of-24 ] .

  In particular ,

  • would we get 5,040 different [ 210 sets-of-24 ] ,
    • when we apply each-and-every one of the Global Set of 5,040 [ Read-Off Orders ] to the 210 Physical [ sets-of-24 ] .

• And our computer-aided analysis here shows that :
  • we can in fact re-group the [ Read-Off Orders ] into groups-of-24 ,
    • and when we apply any [ Read-Off Order ] within the same [ group-of-24 ] ,
      • the resulting [ 210 sets-of-24 8-colors sequences ] will be the same ,

What's next :

• Let us take a quick look at how we would re-gourp the [ Read-Off Orders ] into groups-of-24 , next .

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go to the next section : Section XXXVI - Selection Criteria for re-grouping the [ Read-Off-Orders ]

go to the last section : Section XXXIV - Setting up the 210 [ sets-of-24 ] with Physical Symmetries

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original dated 2011-3-08