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arXiv · 1311.4784

A simpler normal number construction for simple Luroth series

Joseph Vandehey
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Abstract

Champernowne famously proved that the number $0.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)...$ 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.

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Joseph Vandehey. 2013-11-19. A simpler normal number construction for simple Luroth series. https://arxiv.org/abs/1311.4784

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