The original problem, framed in terms of arrays, is to reduce a fraction.
The
equation above is less general.
The less general problem can be restated as reduce a fraction where the numerator and denominator are both the product of factorials.
An example of the original problem is to reduce
(9 * 8 * 8 * 8 * 6 * 4 )/(5 * 3 * 2)
An example of the factorial problem is to reduce
(9! * 8! * 8! * 8! * 6! * 4! )/(5! * 3! * 2!)
Do I understand correctly, are you are interested in the factorial type of problem?
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