Problem 14.1 | Problem 12.11

A First Course in String Theory
 
 
14.1 Counting bosonic states

12.11 Counting symmetric products

~~~

a^{I_1} a^{I_2} ... a^{I_n}

i = 1, 2, ..., n

I_i = 1, 2, ..., k

n is the number of a‘s.

k is the number of different a‘s.

For k=6 and n=9, one of the possible configurations is

a^1 a^2 a^2 a^4 a^4 a^4 a^5 a^6 a^6

The problem is equivalent to that of assigning n balls to k boxes.

Box 1 collects the a‘s with index 1.

Box 2 collects the a‘s with index 2.

— Me@2015-07-13 03:34:32 PM
 
 
 
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