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

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

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Section XXXVI - Selection Criteria for re-grouping the [ Read-Off Orders ]

Summary for the Section :

• In this Section , we shall look very closely at the selection criteria :
  • for grouping the [ Read-Off Orders ] into [ sets-of-24 ] .

  And we shall be using these 4 [ Read-Off Orders ] for our demonstrations here :

  • 

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Applying the [ BANFF Read-Off Order ] :

• Let us now bring-in again the [ 24 QSM-Configurations --- Canadian Rockies Series ] , and
  • do the conversion to the set-of-24 [ 8-colors sequences ] :
    • using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ BANFF Read-Off Order ] ,

      i.e. :

      • 

    to arrive at the new set-of-24 [ 8-colors sequences ] as per the diagram on-the-right , below .

  

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Applying the [ JASPER Read-Off Order ] :

• Let us now bring-in again the [ 24 QSM-Configurations --- Canadian Rockies Series ] , and
  • do the conversion to the set-of-24 [ 8-colors sequences ] :
    • using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ JASPER Read-Off Order ] ,

      i.e. :

      • 

    to arrive at the new set-of-24 [ 8-colors sequences ] as per the diagram on-the-right , below .

  

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A Quick Comparison :

• Let us now bring-in the 2 new sets-of-24 [ 8-colors sequences ] from above :
  • [ BANFF ] on-the-left and [ JASPER ] on-the-right , below .

  

  Do we have a match here ?

  

  • And the answer is YES , we do !

  And let us now quickly name the 24 [ 8-Colors Sequences ] on the left-hand-side diagram :

  • the [ BANFF Twenty-Four ] ,

    for our identification and use immediately below .

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The Selection Criteria for grouping [ Read-Off-Orders ] :

• Let us now apply the [ BANFF / JASPER / REVESTOKE / KAMLOOPS Read-Off Orders ] to [ Configuration Mount Robson ] :
  • and see what we might come-up-with :

  For the [ BANFF Read-off Order ] , we have :

  • 

  For the [ JASPER Read-off Order ] , we have :

  • 

  For the [ REVELSTOKE Read-off Order ] , we have :

  • 

  For the [ KAMLOOPS Read-off Order ] , we have :

  • 

  And we see here that we came-up with one of the [ BANFF Twenty-Four ] 8-colors-sequences as a result every time .

• Let us now do the conversion to the [ 8-colors sequences ] for all four of these [ Read-Off Orders ] :
  • to arrive at this set of 4 diagrams below .

  
  

  And we see here that the [ BANFF Twenty-Four ] showed up exactly on each of the 4 diagrams above .

• Very simply , the selection crtieria here adding a [ Read-Off Order ] into the group is that :
  • Whenever we apply a [ Read-Off Order ] to [ Configuration Mount Robson ] and :
    • one of the [ BANFF Twenty-Four ] 8-color-sequences shows up ;

    then :

    • that particular [ Read-Off Pattern ] may be included into :
      • the [ Banff-Jasper-Revelstoke-Kamloops Group ] of [ Read-Off Orders ] .

  And

  • Since :
    • there are exactly 24 [ 8-colors sequences ] in [ BANFF Twenty-Four ] group , and

    • each [ 8-colors sequence ] will bring-in one-and-only-one matching [ Read-Off Order ] into the group ,

    there-are-and-there-can-be only 24 members in the [ Banff-Japser-Revelstoke-Kamloops Group ] .

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Summarizing :

• In short ,
  • For the 5,040 { [ Read-Off Orders ] starting with Fixed-Position [ FP-1 ] as the lead-off } :
    • these can be re-grouped into 210 x [ sets-of-24 ] ,
      • using the procedure we have just demonstrated above .

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go to the next section : Section XXXVII - Demonstrating the different sets of [ 24 Base Structural Patterns ]

go to the last section : Section XXXV - The Effects of variations in the [ Read-Off Order ]

return to the 8-Colors Combinatorics / Quasi 24-Symmetry HomePage

Original dated 2011-3-08