Permanents and determinants of (0,1) matrices
Jaap Spies
j.spies at hccnet.nl
Mon Nov 3 22:45:46 CET 2003
all at abouthugo.de wrote:
[...]
>
> New sequences:
>
[...]
>
> Maximal permanent of a real non-singular (0,1)-matrix of order n:
> 1 1 3 11 53
>
> Number of real non-singular (0,1)-matrices having maximal permanent=
> a(from previous sequence)
> 1 6 18 96 600
>
>
> Number of different values that can be assumed by the
> permanent of a real non-singular (0,1)-matrix of order n:
> 1 1 3 9 31 (will Jaap Spies compute a(6)?)
>
I will give it a try. The three sequences above can be processed in one go.
> Number of different values that can be assumed by the
> permanent of a real singular (0,1)-matrix of order n:
> 1 2 4 10 32
This can be done before or after the previous action (change one line
in my program).
>
> Smallest positive integer not the permanent of a nXn (0-1) matrix.
> 2 3 5 13 27 119 (last term from Gordon Royle's list)
>
> Maybe also the finite sequences:
>
> How many times does the determinant (D) or permanent (P) of an m*m
> real (0,1)-matrix assume the value n (starting at n=0).
This can be extended to permanents of singular and non-singular matrices
[...]
>
> Please check. Which of these shall I submit?
>
> Hugo
>
I do not know which sequences are interesting enough to be included.
Let the boss speak.
Jaap
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