English

Recovery of cyclic words by their subwords

Discrete Mathematics 2025-12-04 v2 Combinatorics

Abstract

A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in order to uniquely identify a word. In this paper we show that a cyclic word on a binary alphabet can be reconstructed by its scattered subwords of length 34n+4\frac34n+4, and for each nn one can find two cyclic words of length nn which have the same set of scattered subwords of length 34n32\frac34n-\frac32.

Keywords

Cite

@article{arxiv.2412.03289,
  title  = {Recovery of cyclic words by their subwords},
  author = {Sergey Luchinin and Svetlana Puzynina and Michaël Rao},
  journal= {arXiv preprint arXiv:2412.03289},
  year   = {2025}
}