On the Number of Balanced Words of Given Length and Height over a two-Letters alphabet

Nicolas Bédaride (1) , Eric Domenjoud (2) , Damien Jamet (2) , Jean-Luc Rémy (2)

1 IML - Institut de mathématiques de Luminy
2 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery

We exhibit a recurrence on the number of discrete line segments joining two integer points using an encoding of such segments as balanced words of given length and height over the two-letter alphabet {0,1}. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes and provide generating functions in this case. We end by studying the asymptotical behaviour of the previous recurrences.

Mots clés: balanced words; sturmian words; balanced palindromes; discrete line; discrete segment

Domaines: Mathématique discrète [cs.DM]

Nicolas Bédaride, Eric Domenjoud, Damien Jamet, Jean-Luc Rémy. On the Number of Balanced Words of Given Length and Height over a two-Letters alphabet. 6th International Conference on Words - WORDS 2007, Sep 2007, Marseille, France. pp.25-35. ⟨hal-00175027⟩