矩阵行量在受限矩阵上的#P难性证明
#P-hardness proofs of matrix immanants evaluated on restricted matrices
AI总结：
本文证明了特定矩阵类别上计算行量的#P难性，涉及多米诺可铺区域和加权平面有向图邻接矩阵的复杂性分析。
摘要：
我们证明了计算广泛类别的行量，即使在特定矩阵类别上受限时，也是#P难的。具体而言，我们证明当分区λ包含足够大的多米诺可铺区域时，计算0-1矩阵的λ-行量是#P难的，这在某些技术条件下成立。我们还为某些λ-行量的加权平面有向图邻接矩阵给出了难性证明，其中形状λ=(1+λ_d)的大小n满足|λ_d|=n^ε（0<ε<1/2），并且对于某些w，形状λ_d/w可以用1×2多米诺铺满。
英文摘要：
We establish the $\#P$-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing $λ$-immanants of $0$-$1$ matrices is $\#P$-hard whenever the partition~$λ$ contains a sufficiently large domino-tileable region, subject to certain technical conditions. We also give hardness proofs for some $λ$-immanants of weighted adjacency matrices of planar directed graphs, such that the shape $λ= (\mathbf{1} + λ_d)$ has size $n$ such that $|λ_d| = n^\varepsilon$ for some $0 < \varepsilon < \frac{1}{2}$, and such that for some $w$, the shape $λ_d/(w)$ is tileable with $1 \times 2$ dominos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
