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Digits and Beyond

  • Helmut Prodinger
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

This is a survey about digits from a personal point of view. Counting the occurrences of digits (and, more generally, subblocks) is discussed in the context of various positional number systems. The methods to achieve this are Delange's elementary method and Flajolet’s idea to use the Mellin-Perron summation (or integral) formula.

Then we move to problems from Theoretical Computer Science (register function of binary trees, number of exchanges in Baxter’s odd-questions) are also discussed. An open problem from physicists Yekutieli and Mandelbrot can also be treated in that fashion.

Furthermore, we consider representations of numbers where some digits are forbidden. As a representative example, we discuss the Cantor distribution and its moments, asymptotically analyzed by Mellin transforms. Other problems in this context lead to sums involving Bernoulli numbers which can be attacked by analytic Depoissonization.

Very briefly we mention carry propagation, mergesort parameters and jump interpolation search trees.

Keywords

Binary Tree Dirichlet Series Gray Code Probability Letter Exponential Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Helmut Prodinger
    • 1
  1. 1.The John Knopfmacher Centre for Applicable Analysis and Number Theory School of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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