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We focus on combinatorial aspects of the Hilbert series of the cohomologyring of the moduli space of stable pointed curves of genus zero. We show itsgraded Hilbert series satisfies an integral operator identity. This is used togive asymptotic behavior, and in some cases, exact values, of the coefficientsthemselves. We then study the total dimension, that is, the sum of thecoefficients of the Hilbert series. Its asymptotic behavior involves theLambert W function, which has applications to classical tree enumeration,signal processing and fluid mechanics.

Enumerative and asymptotic analysis of a moduli space