Dominating numbers at singular cardinals

We study the generalized dominating number d_μ at a singular cardinal $μ$ of cofinality $κ$. We show two lower bounds: in ZFC, cf([μ]^κ,⊆) ≤ d_μ, and under mild cardinal-arithmetic assumptions, 2<μ ≤ d_μ. We also clarify when d_μ can differ from 2^μ: assuming GCH and κ= cf(μ) > ω, a finite-support iteration of Cohen forcing of length μ⁺⁺ yields d_μ < 2^μ. On the other hand, for κ= cf(μ) = ω, natural $μ$-cc posets force d_μ = 2^μ.