Maximal abelian square-free words of short length

  • Authors:

  • Michael Korn

  • Affiliations:

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

A word is called abelian square-free if it contains no two adjacent subwords which are permutations of each other. An abelian square-free word over an alphabet Σk which cannot be extended to the left or right with letters from Σk while remaining abelian square-free is called a maximal abelian square-free word. We prove, by an explicit construction, that the shortest maximal abelian square-free word over an alphabet of k letters has length at most 6k - 10.