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

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

2010-07-29

arxiv.org/abs/1007.5212v1

published in Discrete Mathematics & Theoretical Computer Science in 2010

Mathematics

Combinatorics

24 pages

Scientific paper

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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