Please help me count.
I have an alphabet with 26 English letters. I can reduce it to 25 letters by representing two of the letters (e.g. O and X) with a new letter (e.g. $\otimes$).
To get down to a 25 letter alphabet I have $26 \choose 2$ possibilities. So 325 possible reductions to alphabet of size 25.
Getting down to an alphabet of size 2 is also pretty easy - I just need to count all possible ways of dividing the alphabet into 2 partitions. That would be $26 \choose 1$ + $26 \choose 2$ + ... + $26 \choose 13$.
In the same way I can reduce my alphabet to any size from 1 to 25. That's 38,754,731 (computed in R like this
How can do the counting for size 3 or 24?
What is the total number of such alphabet reductions?