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 , and for each one can find two cyclic words of length which have the same set of scattered subwords of length .
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}
}