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I prove new subcritical bounds for the $\ell^p$-improving problem alongrestricted subsets of a degenerate curve. The key input is a new paucityestimate for associated inhomogeneous equations which is proven using anelimination method due to Wooley and Parsell--Wooley.

Subcritical paucity and $\ell^p$-improving estimates for finite-type polynomial curves