Periodic balanced binary triangles

Jonathan Chappelon (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: binary triangles; Steinhaus triangles; generalized Pascal triangles; balanced triangles; Steinhaus Problem; periodic triangles; periodic orbits

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Mathématique discrète [cs.DM]

Jonathan Chappelon. Periodic balanced binary triangles. 2017. ⟨hal-01463665v1⟩