Words with the Maximum Number of Abelian Squares

2015/06/11 by Fici, Gabriele, Mignosi, Filippo
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)

paper · doi:10.48550/arxiv.1506.03562

Abstract

An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain Θ(n²) distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length n grows quadratically with n.

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