Maximal number of subword occurrences in a word
Abstract
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We then give upper and lower bounds of minimal subword entropy for words of fixed length in a fixed alphabet, and also showing that minimal subword entropy per letter has a limit value. A better upper bound of minimal subword entropy for a binary alphabet is then given by looking at certain families of periodic words. We also give some conjectures based on experimental observations.
Keywords
Cite
@article{arxiv.2406.02971,
title = {Maximal number of subword occurrences in a word},
author = {Wenjie Fang},
journal= {arXiv preprint arXiv:2406.02971},
year = {2025}
}
Comments
Submitted. Extended abstract accepted by 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Experimental results updated. Comments are welcome