Reconstructing compositions
Abstract
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 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.