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.
>
 
For more references see:
http://www.research.att.com/projects/OEIS?Anum=A003432
Sequence:  1,1,2,3,5,9,32,56,144,320,1458,3645,9477
Hadamard maximal determinant problem: largest determinant of a
(real) {0,1}-matrix of order n.

Hugo Pfoertner