I will use an arbitrary example to show my line of think though it is not completely pieced together. Anyway this is what I have come up with:

for the alphabet (A-Z) n = 26
let k = 3
we want the location of 'HRY'
to find the "start location for 'H', that is the first instance where 'H' is the first character, we use:

sum[(n-x)!/((k-y)!*(n-x-k)!)]as x=0..z
where:
y = the base 1 position of 'H' in 'HRY' (in this case 1)
z = the base 1 position of 'H' in the alphabet

[download]


There are 2 special cases, when k = 2 and when k = n. I will not address k = n because it is uninteresting, and for k = 2 see my previous comment in this thread.

If k > 3, then you would sum across the above equation for each character in the combination making the a appropriate substitution for y, and making a substitution for n such that n' = n - the alphabetic position of the character before it.

Hope that this is not too messy. Also this was done with pen and paper, so it is untested.

In reply to Re^3: Algorithm to convert combinations to bitstring by doowah2004
in thread Algorithm to convert combinations to bitstring by Limbic~Region

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