A First Course in String Theory

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Construct explicitly all the states with and count them, verifying that there are indeed a total of 3200 states.

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The first possibility group includes the cases of one . Since there are 24 species, this group has 24 possibilities.

The second possibility group includes the cases of one with one . (Their order is not important because interchanging the order would create the same state anyway.) Since there are 24 species for each of and , this group has possibilities.

The third possibility group includes the cases of three ‘s. We need to further divide this group into 3 sub-groups.

For the first sub-group, three ‘s are all different:

Since there are 24 species for each , there should be possibilities.

However, since their order is not important, there are repetitions among those possibilities. To eliminate repetitions, we divide the number with . So, this subgroup has

possibilities.

For the second sub-group, two of the three ‘s are identical:

~~There should be possibilities.~~Me@2018-04-20 12:18:38 PM

There should be possibilities.

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For the third sub-group, all three are identical. In other words, there are 24 possibilities.

— Me@2015-06-04 10:19:30 PM

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2015.06.04 Thursday (c) All rights reserved by ACHK