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Generating Functions for the Digital Sum and Other Digit Counting Sequences

Franklin T. Adams-Watters,Frank Ruskey-2009-01-01
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TL;DRAbstract

A numeration system associates a unique string, Ξ(n), with each positive integer n, where each string is over the same finite alphabet. Various digit counting statistics of Ξ(n) are of interest with respect to a numeration system. 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. 1

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A numeration system associates a unique string, Ξ(n), with each positive integer n, where each string is over the same finite alphabet. Various digit counting statistics of Ξ(n) are of interest with respect to a numeration system. 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. 1

Keywords

Numerical digitMathematicsString (physics)AlphabetInteger (computer science)Discrete mathematicsArithmeticCombinatorics

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