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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Contributor : Jonathan Chappelon <>
Submitted on : Friday, November 3, 2017 - 3:29:15 PM
Last modification on : Thursday, January 11, 2018 - 6:27:31 AM
Document(s) archivé(s) le : Sunday, February 4, 2018 - 1:40:45 PM


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  • HAL Id : hal-01463665, version 2
  • ARXIV : 1702.03236


Jonathan Chappelon. Periodic balanced binary triangles. 2017. ⟨hal-01463665v2⟩



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