Permanents and determinants of (0,1) matrices

[all at abouthugo.de]

Edwin Clark <eclark at math.usf.edu> schrieb am 31.10.2003, 20:18:11:
 
> It is tempting to conjecture that the values of the determinant on nxn
> (0,1) matrices are the intergral interval [-(n-1),(n-1)]. However the
> following paper asserts otherwise:
> 
> Craigen, R.(3-WTRL)
> The range of the determinant function on the set of $n\times n$
> $(0,1)$-matrices.
> J. Combin. Math. Combin. Comput. 8 (1990), 161--171.
> --------------------------------------------------------------------------------
> It has been conjectured that the determinant function maps the set of
> $n\times n$ $(0,1)$-matrices onto a set of consecutive integers for any
> given $n$. The author shows this to be false (it does not hold in
> particular for $n=7$) and then further discusses the range of the
> determinant function. Several open questions are given.

I found http://grpmath.prado.com/detspec.html following the link
in http://www.research.att.com/projects/OEIS?Anum=A013588
Prado says:
Theorem:  Let d = det(A), where A is a 7x7 0-1 matrix.  Then
abs(d) \in {0,1,...,17,18,20,24,32}.
His proof is not finished. Are there other sources for this list?

Hugo


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