For $\mathbf{r}:=(r_1,\dots ,r_q)$, an r-factorization of the complete λ-fold h-uniform m-vertex hypergraph $\lambda K_m^h$ is a partition of the edges of $\lambda K_m^h$ into $F_1,\dots ,F_q$ such that each color class $F_i$ is $r_i$-regular and spanning. We prove two results on embedding factorizations. Previously, these results were only known for a few small values of h, and even then only partially. We show that for $n⩾hm$ and $\mathbf{s}:=(s_1,\dots ,s_k)$, the obvious necessary conditions that ensure that an r-factorization of $\lambda K_m^h$ can be embedded into an s-factorization of $\lambda K_n^h$ are also sufficient. This extends Cruse's theorem, Baranyai's theorem, and Häggkvist-Hellgren's theorem. A connected r-factorization is an r-factorization in which each color class is connected. For $n⩾hm$, we establish the necessary and sufficient conditions under which an r-factorization of $\lambda K_m^h$ can be embedded into a connected s-factorization of $\lambda K_n^h$. This extends Walecki's theorem, and Hilton's theorem on embedding Hamiltonian decompositions (take $\lambda =r_1=\dots =r_q=1,h=s_1=\dots =s_k=2$).

为了$\mathbf{r}：=(r_1,\dots ,r_q)$, 一个完整的λ -fold h -uniform m -vertex hypergraph的r -factorization$\lambda {ķ}_{米}^H$是边缘的划分$\lambda {ķ}_{米}^H$进入$F_1,\dots ,F_q$这样每个颜色类$F_{\mathrm{一世}}$是$r_{\mathrm{一世}}$- 常规和跨越。我们证明了嵌入分解的两个结果。以前，这些结果仅对h的几个小值已知，即使这样也只是部分已知。我们证明了$n⩾H米$和$\mathbf{s}：=(s_1,\dots ,s_{ķ})$, 明显的必要条件，确保$\lambda {ķ}_{米}^H$可以嵌入到$\lambda {ķ}_n^H$也足够了。这扩展了 Cruse 定理、Baranyai 定理和 Häggkvist-Hellgren 定理。连接的r因式分解是每个颜色类都连接的 r因式分解。为了$n⩾H米$，我们建立了充分的必要条件，在该条件下，$\lambda {ķ}_{米}^H$可以嵌入到一个连通的 s因式分解中$\lambda {ķ}_n^H$. 这扩展了 Walecki 定理和 Hilton 关于嵌入哈密顿分解的定理（取$\lambda =r_1=\dots =r_q=1,H=s_1=\dots =s_{ķ}=2$）。