Equisum Partitions of Sets of Positive Integers
AbstractLet 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.
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Eggleton, R.B. Equisum Partitions of Sets of Positive Integers. Algorithms 2019, 12, 164.
Eggleton RB. Equisum Partitions of Sets of Positive Integers. Algorithms. 2019; 12(8):164.Chicago/Turabian Style
Eggleton, Roger B. 2019. "Equisum Partitions of Sets of Positive Integers." Algorithms 12, no. 8: 164.
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