# subsequence sum

## Davenport's constant ★★★

Author(s):

For a finite (additive) abelian group , the Davenport constant of , denoted , is the smallest integer so that every sequence of elements of with length has a nontrivial subsequence which sums to zero.

Conjecture

Keywords: Davenport constant; subsequence sum; zero sum

## Gao's theorem for nonabelian groups ★★

Author(s): DeVos

For every finite multiplicative group , let () denote the smallest integer so that every sequence of elements of has a subsequence of length (length ) which has product equal to 1 in some order.

Conjecture   for every finite group .

Keywords: subsequence sum; zero sum

## Few subsequence sums in Z_n x Z_n ★★

Author(s): Bollobas; Leader

Conjecture   For every , the sequence in consisting of copes of and copies of has the fewest number of distinct subsequence sums over all zero-free sequences from of length .

Keywords: subsequence sum; zero sum