On the palindromic decomposition of binary words
Alex Ravsky
TL;DR
This paper establishes a precise formula for the minimal number of palindromes needed to decompose any binary word of a given length and estimates the average number of palindromes in a random binary word.
Contribution
It provides a new exact formula for the minimal palindromic decomposition of binary words and estimates the average number for random words.
Findings
Exact formula for minimal palindromic decomposition K(n)
Estimated average number of palindromes in random binary words
Insights into the structure of binary words based on palindromic decomposition
Abstract
We prove a precise formula for the minimal number K(n) such that every binary word of length can be divided into K(n) palindromes. Also we estimate the average number of palindromes composing a random binary word of the length n.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Coding theory and cryptography