### On the number of balanced words of given length and height over a two letter alphabet

*Nicolas Bedaride, Eric Domenjoud, Damien Jamet, Jean-Luc Rémy*

#### Abstract

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.

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