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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

7 votes
1 answer
303 views

Fraction of subsets with one-third sum

Given is a multiset $A$ of positive real numbers that can be partitioned into three subsets of equal sum (call this sum $s$). Is it true that more than $3/4$ of $A$'s subsets necessarily have sum at …