Generating functions for the digital sum and other digit counting sequences

Franklin T. Adams-Watters.
Frank Ruskey, Department of Computer Science, University of Victoria, Canada.


A numeration system associates a unique string, X(n), with each positive integer n, where each string is over the same finite alphabet. Various digit counting statistics of X(n) are of interest. An example is the digital sum, which is the sum of the digits in the number. We present a unifying framework for deriving identities for the generating functions of such statistics in many of the more popular numeration systems.

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