On the cohomology of moduli spaces of (weighted) stable rational curves

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We give a recursive algorithm for computing the character of the cohomology of the moduli space ₀,ₙ of stable n-pointed genus zero curves as a representation of the symmetric group ₙ on n letters. Using the algorithm we can show a formula for the maximum length of this character. Our main tool is connected to the moduli spaces of weighted stable curves introduced by Hassett.