On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

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

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.

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-Letter Alphabet. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 3 (3), pp.41-62. ⟨10.46298/dmtcs.474⟩. ⟨hal-00580064⟩