I once came across a simple function (probably at mathworld.com) that
dealt with partitions, but now I can't find it. I'll call the
function "f".
Suppose you were to divide the range (0, 1) into N equal partitions
(for example, if N=2, then you have a partition from 0 to 0.5 and
another from 0.5 to 1).
As X ranges from 1 to N (integers only), f(X) generates values in the
range (0, 1) such that exactly one value happens to fall into each
partition, even though the function does not know what "N" is. (The
function isn't perfect, however; for large N it will occasionally miss
a partition, but it still comes close.) At first glance, the function
seems to generate random numbers, even though the sequence is
predetermined and unchanging. Note that the partitions do not get
used up in sequence.
Now my question is, what is the name of the function "f"? Or can you
find the original Mathworld article? |