
zero sum
Pebbling a cartesian product ★★★
Author(s): Graham
We let denote the pebbling number of a graph
.
Conjecture
.

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 ★★★
Let be an (additive) abelian group, and for every
let
.
Conjecture Let
be a matroid on
, let
be a map, put
and
. Then






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
