Periodic balanced binary triangles

Abstract : 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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Submitted on : Thursday, November 23, 2017 - 6:37:26 PM
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Jonathan Chappelon. Periodic balanced binary triangles. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 (3), ⟨http://dmtcs.episciences.org/4101⟩. ⟨10.23638/DMTCS-19-3-13⟩. ⟨hal-01463665v3⟩

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