\#P-hardness of computing matrix immanants are proved for each member of a broad class of shapes and restricted sets of matrices. We prove \#P-hardness of computing $\lambda$-immanants of $0$-$1$ matrices when $\lambda$ has a large domino-tilable part and satisfying some technical conditions. We also give hardness proofs of some $\lambda$-immanants of weighted adjacency matrices of planarly drawable directed graphs, such that the shape $\lambda = (\mathbf{1}+\lambda_d)$ has size $n$ such that $|\lambda_d| = n^{\varepsilon}$ for some $0<\varepsilon<\frac{1}{2}$, and for some $w$, the shape $\lambda_d/(w)$ is tilable with $1\times 2$ dominos.

翻译：我们证明了一类广泛形状和受限矩阵集合中每个成员计算矩阵不变量的#P-困难性。当形状$\lambda$包含一个大的多米诺可铺砌部分并满足某些技术条件时，我们证明了计算$0$-$1$矩阵的$\lambda$-不变量是#P-困难的。我们还给出了某些可平面有向图的加权邻接矩阵的$\lambda$-不变量的困难性证明，其中形状$\lambda = (\mathbf{1}+\lambda_d)$的大小为$n$，且$|\lambda_d| = n^{\varepsilon}$对某个$0<\varepsilon<\frac{1}{2}$成立，并且存在某个$w$使得形状$\lambda_d/(w)$可用$1\times 2$多米诺铺砌。