40 research outputs found
A simpler normal number construction for simple Luroth series
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