Reconstructing compositions Original Research Article

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 image of image can be reconstructed from its set of image-deletions, i.e., the set of all compositions of image contained in image. As there are compositions of image with the same set of image-deletions, this result is best possible.