The maximal length of the period of a periodic word defined by restrictions
Ilya I. Bogdanov, Grigory R. Chelnokov
TL;DR
This paper establishes that the maximum period length of a periodic word constrained by n restrictions is equal to the nth Fibonacci number, revealing a surprising link between combinatorial word properties and Fibonacci numbers.
Contribution
It precisely determines the maximal period length of periodic words under restrictions, connecting it to Fibonacci numbers for the first time.
Findings
Maximal period length equals Fibonacci number
The result applies to words defined by n restrictions
Provides a new combinatorial characterization of periodic words
Abstract
We determine the maximal length of the period of a periodic word defined by restrictions. It happens to be the corresponding Fibonacci number.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Quasicrystal Structures and Properties · Advanced Combinatorial Mathematics