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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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 3 (3), pp.#13. 〈http://dmtcs.episciences.org/4101〉
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https://hal.archives-ouvertes.fr/hal-01463665
Contributeur : Jonathan Chappelon <>
Soumis le : jeudi 23 novembre 2017 - 18:37:26
Dernière modification le : jeudi 11 janvier 2018 - 06:27:31

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  • HAL Id : hal-01463665, version 3
  • ARXIV : 1702.03236

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Jonathan Chappelon. Periodic balanced binary triangles. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 3 (3), pp.#13. 〈http://dmtcs.episciences.org/4101〉. 〈hal-01463665v3〉

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