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this question is mathematical in its sense and considers the following 1D ising spin model

$$s_1s_2s_3....s_{n-1}$$

where $s_i=\pm 1$.

I would like to find the total number of different configurations after reducing symmetry and 'total magnetization'

for example, for a system of $n=4$ the following terms are symmetric $$(-1,+1,+1,+1),(+1,+1,+1,-1)$$

and the following terms have a the same total magnetization ($\sum s_i =2$) $$(+1,-1,+1,+1),(-1,+1,+1,+1)$$

note that there are only two cases of $\sum s_i=2$ because of the symmetry

with these definitions, can I obtain an analytical expression for the total number of state as a function of $n$?

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    $\begingroup$ Which symmetries do you consider? $\endgroup$ Jan 24, 2021 at 22:43
  • $\begingroup$ Can you clarify which states you count together? $\endgroup$
    – ziv
    Mar 11, 2021 at 21:53

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