2024/02/22 by Boonstra, Aafko, Kalle, Charlene
#05C05 #11A63 #11K16 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2402.14500
Let L=(Ld)d ∈ \mathbb N be any ordered probability sequence, i.e., satisfying 0 < Ld+1 ≤ Ld for each d ∈ \mathbb N and ∑d ∈ \mathbb N Ld =1. We construct sequences A = (ai)i ∈ \mathbb N on the countably infinite alphabet \mathbb N in which each possible block of digits α1, …, αk ∈ \mathbb N, k ∈ \mathbb N, occurs with frequency ∏d=1k Lαd. In other words, we construct L-normal sequences. These sequences can then be projected to normal numbers in various affine number systems, such as real numbers x ∈ [0,1] that are normal in GLS number systems that correspond to the sequence L or higher dimensional variants. In particular, this construction provides a family of numbers that have a normal Lüroth expansion.