Characterizing additive systems

Michael Brian Maltenfort*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


An additive system is a collection of sets that gives a unique way to represent either all nonnegative integers, or all nonnegative integers up to some maximum. A structure theorem of de Bruijn gives a certain form for an additive system of infinite size. This form is not, in general, unique. We improve de Bruijn's theorem by finding a unique form for an additive system of arbitrary size. Our proof gives a concrete construction that allows us to test easily whether a collection of sets is an additive system. We also show how to determine most of the structure of an additive system if we are only given its union.

Original languageEnglish (US)
Pages (from-to)132-148
Number of pages17
JournalAmerican Mathematical Monthly
Issue number2
StatePublished - Feb 1 2017

ASJC Scopus subject areas

  • Mathematics(all)


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