Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 48 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 26 tok/s Pro
GPT-5 High 19 tok/s Pro
GPT-4o 107 tok/s Pro
Kimi K2 205 tok/s Pro
GPT OSS 120B 473 tok/s Pro
Claude Sonnet 4 37 tok/s Pro
2000 character limit reached

Rich square-free words (1603.01058v1)

Published 3 Mar 2016 in math.CO and cs.FL

Abstract: A word w is rich if it has |w|+1 many distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word. Pelantov\'a and Starosta (Discrete Math. 313 (2013)) proved that every infinite rich word contains a square. We will give another proof for that result. Pelantov\'a and Starosta denoted by r(n) the length of a longest rich square-free word on an alphabet of size n. The exact value of r(n) was left as an open question. We will give an upper and a lower bound for r(n), and make a conjecture that our lower bound is exact. We will also generalize the notion of repetition threshold for a limited class of infinite words. The repetition thresholds for episturmian and rich words are left as an open question.

Citations (7)

Summary

We haven't generated a summary for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Lightbulb On Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube