# The additive basis conjecture

 Importance: High ✭✭✭
 Author(s): Jaeger, Francois Linial, Nathan Payan, Charles Tarsi, Michael
 Subject: Combinatorics » Matrices
 Keywords: additive basis matrix
 Recomm. for undergrads: no
 Posted by: mdevos on: March 8th, 2007
Conjecture   For every prime , there is a constant (possibly ) so that the union (as multisets) of any bases of the vector space contains an additive basis.

Definition: Let be a finite dimensional vector space over the field . We call a multiset with elements in an additive basis if for every , there is a subset of which sums to .

It is worth noting that this conjecture would also imply that every -edge-connected graph has a nowhere-zero 3-flow, thus resolving The weak 3-flow conjecture.