# [seqfan] Re: nonsingular binary matrices

Brendan McKay Brendan.McKay at anu.edu.au
Mon May 25 10:35:34 CEST 2020

```Dear Neil,

Yes, I checked it.  I'll change the definition and add one more value to
boot!

Cheers, Brendan.

On 25/5/20 6:24 pm, Neil Sloane wrote:
> Dear Brendan, It seems to me very likely that what you say is correct, and
> that A224879 refers to matrices over GF(2), while the other entry refers to
> real matrices with entries  0 and 1. Could I ask you to please make the
> necessary changes to those entries?
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
>
> On Mon, May 25, 2020 at 2:50 AM Brendan McKay <Brendan.McKay at anu.edu.au>
> wrote:
>
>> I'm looking at:
>>
>> A116976
>> 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
>>
>> A224879
>> 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.
>>
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
```