[seqfan] nonsingular binary matrices

Brendan McKay Brendan.McKay at anu.edu.au
Mon May 25 08:50:36 CEST 2020

I'm looking at:

Number of regular n X n matrices with rational entries equal to 0 or 1, 
up to row and column permutations.
1, 2, 8, 61, 1153, 64310, 11352457

Number of inequivalent nonsingular n X n binary matrices, where 
equivalence means permutations of rows or columns.
1, 2, 7, 51, 885, 44206, 6843555

I understand that "regular" means the same as "nonsingular", but since 
"regular" is minority lingo for this property I propose to rename 
A116976 to use "nonsingular" (or both).

Now we have the problem that the descriptions are the same but the 
numbers are different.  According to my calculations, A116976 is the one 
matching the description.

Looking at one of the references given for A224879 
<https://arxiv.org/pdf/1205.5062.pdf>, it appears that the field of 2 
elements is involved.  Perhaps these are matrices non-singular over 
GF(2)? I haven't checked this, so if someone can check it and clarify 
the definition that would be good.

Cheers, Brendan.

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