Extremal problems for subset divisors

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Abstract

Let A be a set of n positive integers. We say that a subset B of A is a divisor of A, if the sum of the elements in B divides the sum of the elements in A. We are interested in the following extremal problem. For each n, what is the maximum number of divisors a set of n positive integers can have? We determine this function exactly for all values of n. Moreover, for each n we characterize all sets that achieve the maximum. We also prove results for the k-subset analogue of our problem. For this variant, we determine the function exactly in the special case that n = 2k. We also characterize all sets that achieve this bound when n = 2k.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalElectronic Journal of Combinatorics
Volume21
Issue number1
Publication statusPublished - 28 Feb 2014
Externally publishedYes

Keywords

  • Exact enumeration
  • Extremal combinatorics

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