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Algorithms, Vol. 12, Pages 164: Equisum Partitions of Sets of Positive Integers (2019)

Roger B. Eggleton

MDPI

In: Algorithms

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Publication Date: 2019

Description: Let V be a finite set of positive integers with sum equal to a multiple of the integer b . When does V have a partition into b parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, albeit incomplete, answers for the following classes of set V , where n is a given positive integer: (1) an initial interval { a ∈ ℤ + : a ≤ n } ; (2) an initial interval of primes { p ∈ ℙ : p ≤ n } , where ℙ is the set of primes; (3) a divisor set { d ∈ ℤ + : d | n } ; (4) an aliquot set { d ∈ ℤ + : d | n , d 〈 n } . Open general questions and conjectures are included for each of these classes.

Electronic ISSN: 1999-4893

Topics: Computer Science

Published by MDPI

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