## Bédaride, Nicolas and Domenjoud, Eric and Jamet, Damien and Rémy, Jean-Luc - On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

dmtcs:474 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 3
On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

Authors: Bédaride, Nicolas and Domenjoud, Eric and Jamet, Damien and Rémy, Jean-Luc

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.

Source : oai:HAL:hal-00580064v1
Volume: Vol. 12 no. 3
Published on: January 1, 2010
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]