Equisum Partitions of Sets of Positive Integers†
School of Mathematical and Physical Sciences, University of Newcastle, Newcastle 2308, Australia
Dedicated to Richard Guy, for his 103rd Birthday, one of many primes of his life.
Received: 12 July 2019 / Revised: 5 August 2019 / Accepted: 7 August 2019 / Published: 11 August 2019
PDF [260 KB, uploaded 22 August 2019]
be a finite set of positive integers with sum equal to a multiple of the integer
. When does
have a partition into
parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, albeit incomplete, answers for the following classes of set
is a given positive integer: (1) an initial interval
; (2) an initial interval of primes
is the set of primes; (3) a divisor set
; (4) an aliquot set
. Open general questions and conjectures are included for each of these classes.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
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.
Eggleton, Roger B. 2019. "Equisum Partitions of Sets of Positive Integers." Algorithms 12, no. 8: 164.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.