Geodesic
Periodic balanced binary triangles
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3.

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A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$. A binary triangle is said to be balanced if the absolute difference between the numbers of zeroes and ones that constitute this triangle is at most $1$. In this paper, the existence of balanced binary triangles of size $n$, for all positive integers $n$, is shown. This is achieved by considering periodic balanced binary triangles, that are balanced binary triangles where each row, column or diagonal is a periodic sequence. 
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     author = {Chappelon, Jonathan},
     title = {Periodic balanced binary triangles},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2017-2018},
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     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-13/}
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Chappelon, Jonathan. Periodic balanced binary triangles. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3. doi : 10.23638/DMTCS-19-3-13. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-13/

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