For two frames \(\{\phi _i\}_{i \in {\mathcal {I}}}\) and \(\{\psi _i\}_{i\in {\mathcal {I}}}\), the family \(\{\phi _i\}_{i \in \sigma } \cup \{\psi _i\}_{i \in \sigma ^c}\) is called a weaving, where \({\mathcal {I}}\) is a countable index set and \(\sigma \subset {\mathcal {I}}\). Two frames \(\{\phi _i\}_{i \in {\mathcal {I}}}\) and \(\{\psi _i\}_{i\in {\mathcal {I}}}\) are called woven if all their weavings are frames with the same frame bounds. The concept of this manuscript is motivated by an important and interesting problem which is, under what conditions the frames \(\{\phi _i\}_{i \in {\mathcal {I}}}\) and \(\{\phi _{\pi (i)}\}_{i\in {\mathcal {I}}}\) are woven for the separable Hilbert space H, where \(\pi \) is a permutation function on \({\mathcal {I}}\). In this paper, the effect of reordering of the elements of weavings for frames is studied. In particular, full spark frames and m-uniform excess frames are studied. Also, an interesting characterization of reordered weavings by orthogonal projections is given. Finally, the effects of perturbations are considered.

对于两个帧\（\ {\ phi _i \} _ {i \ in {\ mathcal {I}}} \）和\（\ {\ psi _i \} _ {i \ in {\ mathcal {I}}} \），家族\（\ {\ phi _i \} _ {i \ in \ sigma} \ cup \ {\ psi _i \} _ {i \ in \ sigma ^ c} \）被称为编织，其中\ （{\ mathcal {I}} \）是可计数的索引集和\（\ sigma \ subset {\ mathcal {I}} \）。两个帧\（\ {\ phi _i \} _ {i \在{\ mathcal {I}}} \\）和\（\ {\ psi _i \} _ {i \ in {\ mathcal {I}}} \\ ），如果所有编织都是具有相同框架范围的框架，则称为“编织”。该手稿的概念受到一个重要且有趣的问题的启发，即在什么条件下，框架\（\ {\ phi _i \} _ {i \ in {\ mathcal {I}}} \）和\（\ {\ phi _ {\ pi（i）} \} _ {i \ in {\ mathcal {I}}} \\）是为可分离的希尔伯特空间H编织的，其中\（\ pi \）是一个置换\（{\ mathcal {I}} \）上的函数。在本文中，研究了框架编织元素的重新排序的效果。特别是，研究了完整的火花框架和m均匀的多余框架。另外，给出了通过正交投影对重新排序的编织进行有趣的表征。最后，考虑摄动的影响。