Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Completely uniformly distributed sequences based on de Bruijn sequences
HTML articles powered by AMS MathViewer

by Emilio Almansi and Ver贸nica Becher HTML | PDF
Math. Comp. 89 (2020), 2537-2551 Request permission

Abstract:

We study a construction published by Donald Knuth in 1965 yielding a completely uniformly distributed sequence of real numbers. Knuth鈥檚 work is based on de Bruijn sequences of increasing orders and alphabet sizes, which grow exponentially in each of the successive segments composing the generated sequence. In this work we present a similar, albeit simpler, construction using linearly increasing alphabet sizes, and we give an elementary proof showing that the generated sequence is also completely uniformly distributed. In addition, we present an alternative proof of the same result based on Weyl鈥檚 criterion.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 11-04, 11K36, 68-04
  • Retrieve articles in all journals with MSC (2010): 11-04, 11K36, 68-04
Additional Information
  • Emilio Almansi
  • Affiliation: Departamento de Computaci贸n, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
  • Email: ealmansi@gmail.com
  • Ver贸nica Becher
  • Affiliation: Departamento de Computaci贸n, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires & ICC CONICET, Argentina
  • MR Author ID: 368040
  • Email: vbecher@dc.uba.ar
  • Received by editor(s): September 24, 2019
  • Received by editor(s) in revised form: December 29, 2019, and January 4, 2020
  • Published electronically: April 6, 2020
  • Additional Notes: Supported by Universidad de Buenos Aires and CONICET, Argentina
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2537-2551
  • MSC (2010): Primary 11-04, 11K36; Secondary 68-04
  • DOI: https://doi.org/10.1090/mcom/3534
  • MathSciNet review: 4109577