Constructions of normal numbers with infinite digit sets
Year: 2025
Type: article
Abstract: Let L = ( L d ) d ∈ N be any ordered probability sequence, i.e., satisfying 0 < L d + 1 ≤ L d for each d ∈ N and ∑ d ∈ N L d = 1 . We construct sequences A = ( a i ) i ∈ N on the countably infinite alphabet N in which each possible block of digits α 1 , … , α k ∈ N , k ∈ N , occurs with frequency ∏ d = 1 k L α d . 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.
Source: Journal of Complexity
Authors: Aafko Boonstra, Charlene Kalle
Institutions: Vrije Universiteit Amsterdam, Leiden University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,680
OpenAlex ID: W4409197108