A simpler normal number construction for simple Luroth series
Number Theory
2013-11-20 v1
Abstract
Champernowne famously proved that the number formed by concatenating all the integers one after another is normal base 10. We give a generalization of Champernowne's construction to various other digit systems, including generalized L\"uroth series with a finite number of digits. For these systems, our construction simplifies a recent construction given by Madritsch and Mance. Along the way we give an estimation of the sum of multinomial coefficients above a tilted hyperplane in Pascal's simplex, which may be of general interest.
Keywords
Cite
@article{arxiv.1311.4784,
title = {A simpler normal number construction for simple Luroth series},
author = {Joseph Vandehey},
journal= {arXiv preprint arXiv:1311.4784},
year = {2013}
}