Re Permanents of (+1,-1) matrices

[Jaap Spies]

N. J. A. Sloane wrote:
> Thanks to everyone who replied.  To summarize, let A
> be a nonsingular +1,-1  n X n matrix.  The conjecture appears
> to be that for n >= 5 the max permanent of A is given by
> the following (new) sequence:
> 
> %I A087981
> %S A087981 0,2,4,24,128,880,6816,60032,589312
> %N A087981 Permanent of the n X n (+1,-1)-matrix with exactly n-1 -1s on the diagonal.
> %C A087981 It is conjectured by Kraeuter and Seifter that for n >= 5 this is the maximum possible value for the permanent of a nonsingular n X n (+1,-1)-matrix with exactly n-1 -1's on the diagonal. 
> %C A087981 I don't know for what values of n this has been confirmed. As Edwin Clark points out, it is certainly false for n = 4. - njas
> %C A087981 The maximum possible value for the permanent of a singular n X n (+1,-1)-matrix is obviously n!.
> %D A087891 A. R. Kraeuter and N. Seifter, Some properties of the permanent of (1,-1)-matrices,  Linear and Multilinear Algebra 15 (1984), 207-223.
> %D A087981 N. Seifter, Upper bounds for permanents of (1,-1)-matrices, Israel J. Math. 48 (1984), 69-78.
> %D A087891 Edward Tzu-Hsia  Wang, On permanents of (1,-1)-matrices, Israel J. Math. 18 (1974), 353-361.
> %O A087981 2,2
> %K A087981 nonn,easy,more
> %A A087981 Gordon Royle (gordon(AT)csse.uwa.edu.au), Oct 28 2003
> 
> But what is the max permanent for n <= 4 ?  For 
> n =  1  2  3  4    we have
>      1  0  6  x     where thanks to Ed Clark we know x >= 8
> 
> It remains to see if 8 is the max permanent of a 4x4 nonsingular
> +1,-1 matrix - could someone please do that computation?
> 
> 
> NJAS
> 
> .
> 
I do have some more. At the moment up to n=25, with my 'new alg' (to be published)
for the permanent:

n =  2:                         0
n =  3:                         2
n =  4:                         4
n =  5:                        24
n =  6:                       128
n =  7:                       880
n =  8:                      6816
n =  9:                     60032
n = 10:                    589312
n = 11:                   6384384
n = 12:                  75630080
n = 13:                 972387328
n = 14:               13483769856
n = 15:              200571078656
n = 16:             3185540657152
n = 17:            53800242216940
n = 18:           962741176500224
n = 19:         18195808235851328
n = 20:        362183230599829504
n = 21:       7572922094356201472
n = 22:     165945771114706763776
n = 23:    3802923921409419771904
n = 24:   90965940198950249168896
n = 25: 2267151124762193502928896



Jaap Spies