Constructive Bounds on Ordered Factorizations

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Constructive Bounds on Ordered Factorizations

The number of ways to factor a natural number into an ordered product of integers, each factor greater than one, is called the ordered factorization of n and is denoted H(n). We show upper and lower bounds on H(n) with explicit constructions.

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On the number of ordered factorizations of natural numbers

We study the number of ways to factor a natural number n into an ordered product of integers, each factor greater than one, denoted by H (n). This counting function from number theory was shown by Newberg and Naor (Adv. Appl. Math. 14 (1993) 172–183) to be a lower bound on the number of solutions to the so-called probed partial digest problem, which arises in the analysis of data from experimen...

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ژورنال

عنوان ژورنال: SIAM Journal on Discrete Mathematics

سال: 2005

ISSN: 0895-4801,1095-7146

DOI: 10.1137/s0895480104445861