# zero sum

## Pebbling a cartesian product ★★★

Author(s): Graham

We let denote the pebbling number of a graph .

Conjecture   .

Keywords: pebbling; zero 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

## Bases of many weights ★★★

Author(s): Schrijver; Seymour

Let be an (additive) abelian group, and for every let .

Conjecture   Let be a matroid on , let be a map, put and . Then

Keywords: matroid; sumset; 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 ★★

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

## Olson's Conjecture ★★

Author(s): Olson

Conjecture   If is a sequence of elements from a multiplicative group of order , then there exist so that .

Keywords: zero sum