counting complexity class

If $𝒩𝒞$ is a complexity class associated with non-deterministic machines then $\mathrm{\#}𝒞=\{\mathrm{\#}R\mid R\in 𝒩𝒞\}$ is the set of counting problems associated with each search problem in $𝒩𝒞$. In particular, $\mathrm{\#}𝒫$ is the class of counting problems associated with $𝒩𝒫$ search problems.