Improved Bounds on the Length of Maximal Abelian Square-free Words

A word is abelian square-free if it does not contain two adjacent subwords which are permutations of each other. Over an alphabet k on k letters, an abelian squarefree word is maximal if it cannot be extended to the left or right by letters from k and remain abelian square-free. Michael Korn proved that the length (k) of a shortest maximal abelian square-free word satisfies 4k - 7 (k) 6k - 10 for k 6. In this paper, we refine Korn's methods to show that 6k-29 (k) 6k-12 for k 8.

• Type: Journal
• Year: 2004
• Where: COMBINATORICS
• Authors: Evan M. Bullock
• Keywords: Abelian Square-free Word, Abelian Squarefree Word, COMBINATORICS 2004, Square-free