A zero-sum sequence over an Abelian group 
is a finite sequence of elements
of 
whose sum is the identity element. In additive
combinatorics, a sequence is treated as a finite multiset, so terms may repeat and order is immaterial (Gao
and Geroldinger 2006, p. 337).
For a finite Abelian group of group exponent 
, the Erdős-Ginzburg-Ziv
constant 
is the least length forcing a zero-sum subsequence of exactly 
terms, while 
is the least length forcing a nonempty zero-sum subsequence
of at most 
terms. These differ from the Davenport constant,
which imposes no upper limit on the length of the nonempty zero-sum subsequence,
and from the Gao constant, which prescribes 
terms.
The extremal inverse questions ask what sequences of lengths 
and 
can avoid the respective zero sums. Property
C and property D describe proposed repeated-block
structures for these sequences (Wang and Zeng 2026b).
A counting refinement is the Bialostocki-Lotspeich conjecture, proved by Wang and Zeng (2026a).
