The Erdős-Nicolas-Sárközy conjecture concerns the number 
of nonempty admissible sets
contained in 
. An admissible set
here requires that equal-sum subsets have equal cardinal
number. The conjecture asserts that 
(Erdős et al. 1991), where
denotes big-Theta notation.
Wang and Yang (2026) proved that there are absolute constants 
such that
 |
for every integer 
. The same bounds hold for the number of admissible
sets whose maximum is exactly 
. The counting problem is distinct from maximizing the cardinal
number of an admissible set.
