Integer Partitioning May Be Useful for Developing Statistical Models

I never studied number theory in school, so my approach to the problem may be a bit different.
I approached the problem by tabulating results and then searching for patterns. I never discovered an algebraic answer, but was able to develop a fractal approach to solving partition problems. That means that my answers are in terms of table coordinates. The partition table is easy to generate due to the fractal nature of the pattern. I've also learned how to answer the question of how many partitions may contain a subgroup of values or how many partitions that contain a given number of parts also contain certain values. I learned that I could partition non-integers, because if P(K) u=1 means the partition of K with one being the smallest value for any part, then P(K) u = P(cK) cu. This means that if u=0.1, I can find the answer by assigning c=10. In the practical world, all results are reported to a number of significant figures and data usually contains only positive values, so the number of ways to obtain a value in the practical world is actually finite, not infinite. If K is a mean value, all possible ways to obtain that mean can be found if we define the number of parts permitted and the number of significant figures. By looking at the frequency of parts with a given value, I can also graph the distribution of values without any restriction on standard deviation.

Note by John Leach
1 year, 10 months ago

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