# matrix

## The Alon-Tarsi basis conjecture ★★

Author(s): Alon; Linial; Meshulam

Conjecture   If are invertible matrices with entries in for a prime , then there is a submatrix of so that is an AT-base.

Keywords: additive basis; matrix

## The permanent conjecture ★★

Author(s): Kahn

Conjecture   If is an invertible matrix, then there is an submatrix of so that is nonzero.

Keywords: invertible; matrix; permanent

## The additive basis conjecture ★★★

Author(s): Jaeger; Linial; Payan; Tarsi

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.

Keywords: additive basis; matrix