论文标题
关于对称的伪树状功能：分解，内核和应用
On Symmetric Pseudo-Boolean Functions: Factorization, Kernels and Applications
论文作者
论文摘要
对称伪树生函数是从布尔元组到实数的地图，在输入变量互换下是不变的。我们证明，任何此类功能都可以等效地表示为功率序列或分解。伪树生函数的内核是导致该函数相同消失的所有输入的集合。任何$ n $ - 可变性对称的伪树状函数$ f（x_1，x_2，\ dots，x_n）$具有至少对应于一个$ n $ n $ affine超平面的内核，每个超平面均由约束$ \ sum_ $ \ sum_ {l = 1}^n x_l = 1}^n x_l =λ$ for $ c $ n o $ n n o $ can cance $ cans c。我们使用这些结果来分析自旋玻璃函数文献（ISING模型），量子信息和张量网络中出现的对称伪树生功能。
A symmetric pseudo-Boolean function is a map from Boolean tuples to real numbers which is invariant under input variable interchange. We prove that any such function can be equivalently expressed as a power series or factorized. The kernel of a pseudo-Boolean function is the set of all inputs that cause the function to vanish identically. Any $n$-variable symmetric pseudo-Boolean function $f(x_1, x_2, \dots, x_n)$ has a kernel corresponding to at least one $n$-affine hyperplane, each hyperplane is given by a constraint $\sum_{l=1}^n x_l = λ$ for $λ\in \mathbb{C}$ constant. We use these results to analyze symmetric pseudo-Boolean functions appearing in the literature of spin glass energy functions (Ising models), quantum information and tensor networks.
