On investigations regarding selfdual {0,1}matrices.
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Detailed Description
On investigations regarding selfdual {0,1}matrices.
 Todo:
 Smallest selfdual but not selfpolar matrix

See the "Experiment" in ComputerAlgebra/CombinatorialMatrices/Lisp/Isomorphisms.mac.

Interesting also to determine the number of selfdual and selfpolar matrices.

Easy cases (showing the quotient #selfdual/#all):

n=0: 1/1

n=1: 2/2

n=2: 12/16

n=3: 248/512

n=4: 15428/65536
In each case every selfdual matrix was selfpolar.

n = 5:

Random sampling yields 16686/213822.

By a C++ implementation we could run through all cases (see OKlib/Combinatorics/plans/general.hpp).

n = 6:

Random sampling: 944/58092.

n = 7:

Random sampling: 15/6060.

Another run with set_random(0): 171/100037.

n = 8:

With default setting: 0/2567.

With set_random(0): 1/2976 (segfault at interrupt).

With set_random(1): 2/11720 (with Ecl; after several interrupts lost connection).

It seems that for small n (n <= 5) there are no selfdual but not selfpolar matrices, while for bigger n selfdual matrices become very rare (so that a random search for them won't succeed).
Definition in file SelfDuality.hpp.