![](/files/happy5.png)
invertible
The permanent conjecture ★★
Author(s): Kahn
Conjecture If
is an invertible
matrix, then there is an
submatrix
of
so that
is nonzero.
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ n \times n $](/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png)
![$ n \times n $](/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png)
![$ B $](/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png)
![$ [A A] $](/files/tex/d1e9d82c656535b507686183e640178057fae455.png)
![$ perm(B) $](/files/tex/611c52c475fe4a5ad9a2c30107f439f4ff88506f.png)
Keywords: invertible; matrix; permanent
A nowhere-zero point in a linear mapping ★★★
Author(s): Jaeger
Conjecture If
is a finite field with at least 4 elements and
is an invertible
matrix with entries in
, then there are column vectors
which have no coordinates equal to zero such that
.
![$ {\mathbb F} $](/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png)
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ n \times n $](/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png)
![$ {\mathbb F} $](/files/tex/0996310fb2d1a49c39f098ca07ee5323bf728b79.png)
![$ x,y \in {\mathbb F}^n $](/files/tex/817584f802a24b69508ae913bf47b34d6ff78ca8.png)
![$ Ax=y $](/files/tex/6fc49872cdb030ca09b427d20b9fd3b1d3873641.png)
Keywords: invertible; nowhere-zero flow
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