论文标题
置换组的分离直接产品分解
Disjoint direct product decomposition of permutation groups
论文作者
论文摘要
令$ h \ leq s_n $为轨道$ω_1，ω_2，\ ldots，ω_k$的不及物子组。当然，$ h $是其在每个轨道上投影的直接乘积的细分产品，$ h | _ {ω_1} \ times h | _ {ω_2} \ times \ times \ ldots \ times \ times h | _ | _ {ω_k} $。在这里，我们提供了一个多项式时间算法，用于计算$ h $ orbits的最佳分区$ p $，以便$ h = \ prod_ {c \ in p} h | _c $ in p} h | _c $，并在某些应用中演示其有用性。
Let $H \leq S_n$ be an intransitive group with orbits $Ω_1, Ω_2, \ldots ,Ω_k$. Then certainly $H$ is a subdirect product of the direct product of its projections on each orbit, $H|_{Ω_1} \times H|_{Ω_2} \times \ldots \times H|_{Ω_k}$. Here we provide a polynomial time algorithm for computing the finest partition $P$ of the $H$-orbits such that $H = \prod_{c \in P} H|_c$ and demonstrate its usefulness in some applications.
