# [seqfan] Re: nonsingular binary matrices

Neil Sloane njasloane at gmail.com
Mon May 25 10:24:47 CEST 2020

```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.
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.
>
>
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>
```