On Unique-Factorization Combinatorics via the Pascal Triangle

by Frank C. Fung ( 1st published in October, 2012. )

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Section XX - Creating the 10 x 10 [ Z Matrix ]

Summary for the Section :

• In this Section , we shall create the 10 x 10 [ Z Matrix ] .

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Creating the [ Z Matrix ] :

• Let us bring-in again the [ ALPHA Matrix ] and the [ ETA Matrix ] from the previous 2 Sections :
  • as shown below with [ ALPHA ] on-the-left and [ ETA ] on-the-right .

  

• We then create the [ Z Matrix ] given by :
  • [ Z ] = [ ALPHA ] x [ ETA ]

  We then have the resultant [ Z Matrix ] as shown in the diagram on-the-left below .

  

  • And the diagram on-the-right above then simply shows the same [ Z Matrix ] ,
    • but colored differently in preparation for the next Section to follow .

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What is the [ Z Matrix } :

• Let us just state here that :
  • For the position at { Row [ T ] , Column [ H ] } of the [ Z Matrix ] :
    • the value at the position is then :
      • The number of { Category [ T ] composite numbers } that can be formulated
        • with a initial set of [ H ] distinct-and-different [ prime numbers ] .

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go to the next section : Section XXI - Symmetry Considerations for the [ Z Matrix ]

go to the last section : Section XIX - Creating the 10 x 10 [ ETA Matrix ]

return to the Unique-Factorization Combinatorics HomePage

Original dated 2012-10-08