where all $B_i$ are simple crystals. For a classical weight $\Lambda$ the set of unrestricted paths is defined as $$\label{p}
{\mathcal{P}}(B,{\Lambda})=\{ b\in B \mid {\mathrm{wt}}(b)={\Lambda}\}.$$ For a dominant classical weight ${\Lambda}$ the set of classically restricted paths is $$\label{p'}
{\mathcal{P}}'(B,{\Lambda})=\{ b\in B \mid \text{${\mathrm{wt}}(b)={\Lambda}$ and $e_ib=0$ for all 
 $i\in J$} \}$$ and the set of level-restricted paths for $\ell\in{\mathbb{N}}$ is $$\label{pl}
{\mathcal{P}}^\ell(B,{\Lambda})=\{ b\in B \mid \text{${\mathrm{wt}}(b)={\Lambda}$, $e_ib=0$ for all 
 $i\in J$ and $e_0^{\ell+1}b=0$}\}.$$

The corresponding one-dimensional configuration sums are the generating functions of these sets of paths with energy/coenergy statistics. The one-dimensional sums $$\label{super}
\begin{split}
S(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}(B,{\Lambda})} q^{D_B(b)}\\
{\overline{S}}(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}(B,{\Lambda})} q^{{\overline{D}}_B(b)}
\end{split}$$ are called supernomials, whereas $$\label{kostka}
\begin{split}
X(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}'(B,{\Lambda})} q^{D_B(b)}\\
{\overline{X}}(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}'(B,{\Lambda})} q^{{\overline{D}}_B(b)}
\end{split}$$ are the classically restricted configuration sums or generalized Kostka polynomials, and $$\label{lkostka}
\begin{split}
X^\ell(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}^\ell(B,{\Lambda})} q^{D_B(b)}\\
{\overline{X}}^\ell(B,{\Lambda})&=\sum_{b\in {\mathcal{P}}^\ell(B,{\Lambda})} q^{{\overline{D}}_B(b)}
\end{split}$$ are the level-$\ell$ restricted configuration sums or $\ell$-generalized Kostka polynomials.

The classically restricted configurations sums are graded tensor product multiplicities. The level-restricted configuration sums are graded level $\ell$ fusion coefficients. Let $B_{{\Lambda}'}$ denote the crystal corresponding to the affine irreducible highest weight representation $V({\Lambda}')$. By the Verlinde formula [@V], the fusion coefficient is the coefficient of $B_{{\Lambda}'}$ of weight ${\Lambda}' ={\Lambda}+\ell{\Lambda}_0$ in the decomposition of 