An admissible set in the additive sense of Erdős et al. (1991) is a finite set 
of positive integers such that two subsets
of 
with the same sum always have the same
cardinal number. This allows different subsets
of equal size to have equal sums. For example, 
is admissible even though 
. The condition differs from requiring all subset sums
to be distinct.
The Erdős-Nicolas-Sárközy conjecture concerns the number of these sets contained in 
.
