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Critical exponent of ternary words with few distinct palindromes

Ľubomíra Dvořáková, Lucas Mol, Pascal Ochem

Abstract

We study infinite ternary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponent.

Critical exponent of ternary words with few distinct palindromes

Abstract

We study infinite ternary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponent.

Paper Structure

This paper contains 11 sections, 14 theorems, 29 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Negative results
  4. Exponential cases
  5. First polynomial case
  6. Second polynomial case
  7. Critical exponent of g(h omega(0))
  8. Bispecial factors in h omega(0)
  9. Shortest return words to bispecial factors in h omega(0)
  10. Bispecial factors in g(h omega(0))
  11. Overpals and letter patterns

Key Result

Theorem 1

There exists no infinite ternary $\beta$-free word containing only $p$ palindromes for the following pairs $(p, \beta)$.

Theorems & Definitions (27)

  • Theorem 1
  • proof
  • Lemma 2
  • Theorem 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • proof
  • Lemma 6
  • ...and 17 more