357 research outputs found
Extremal Problems for Subset Divisors
Let be a set of positive integers. We say that a subset of is
a divisor of , if the sum of the elements in divides the sum of the
elements in . We are interested in the following extremal problem. For each
, what is the maximum number of divisors a set of positive integers can
have? We determine this function exactly for all values of . Moreover, for
each we characterize all sets that achieve the maximum. We also prove
results for the -subset analogue of our problem. For this variant, we
determine the function exactly in the special case that . We also
characterize all sets that achieve this bound when .Comment: 10 pages, 0 figures. This is essentially the journal version of the
paper, which appeared in the Electronic Journal of Combinatoric
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