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Combinatorics » Matrices

The permanent conjecture ★★

Author(s): Kahn

Conjecture   If $ A $ is an invertible $ n \times n $ matrix, then there is an $ n \times n $ submatrix $ B $ of $ [A A] $ so that $ perm(B) $ is nonzero.

Keywords: invertible; matrix; permanent

Posted by mdevos
updated March 8th, 2007
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Combinatorics » Matrices

A nowhere-zero point in a linear mapping ★★★

Author(s): Jaeger

Conjecture   If $ {\mathbb F} $ is a finite field with at least 4 elements and $ A $ is an invertible $ n \times n $ matrix with entries in $ {\mathbb F} $, then there are column vectors $ x,y \in {\mathbb F}^n $ which have no coordinates equal to zero such that $ Ax=y $.

Keywords: invertible; nowhere-zero flow

Posted by mdevos
updated March 8th, 2007
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