重构组合物
Reconstructing compositions
摘要：
我们考虑的问题，重建一个整数的组成，从他们的子组成，这是提出了Raykova（虽然伪装成一个问题分层排列）。我们证明了n个\ge 3 k +1的每个组合w都可以从其k-缺失的集合中重建，即，包含在w中的n-k的所有合成的集合。由于存在具有相同的k-缺失集合的3 k的组合物，因此该结果是最可能的。
英文摘要：
We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutations). We show that every composition w of n\ge 3k+1 can be reconstructed from its set of k-deletions, i.e., the set of all compositions of n-k contained in w. As there are compositions of 3k with the same set of k-deletions, this result is best possible.
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。
