For every genus g and one or more punctures, the mixed Hodge numbers of all unordered configuration spaces are encoded by a single rational generating function.
Betti and Hodge numbers of configuration spaces of a punctured elliptic curve from its zeta functions
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Hilbert Series for Configuration Spaces of Punctured Surfaces
For every genus g and one or more punctures, the mixed Hodge numbers of all unordered configuration spaces are encoded by a single rational generating function.