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
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.02971
- arXiv:
- arXiv:2406.02971
- Bibcode:
- 2024arXiv240602971F
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics
- E-Print:
- Extended abstract accepted by 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Comments are welcome