Maximal number of subword occurrences in a word
<|reference_start|>Maximal number of subword occurrences in a word: 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<|reference_end|>
@article{fang2024maximal,
    title={Maximal number of subword occurrences in a word},
    author={Wenjie Fang},
    journal={arXiv preprint arXiv:2406.02971},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.02971},
    primaryClass={math.CO cs.DM}
}