The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Merge this and GC-set into Closure with a twist and redirect thereto. Avi 03:55, 26 March 2007 (UTC)[reply]

Cwatset[edit]

Unintelligible, probably with typos carried over from the original source, [1]; see Talk:Cwatset. Perhaps a new article should be written on the subject, but it would have to be reliably sourced and not nonsense. Quuxplusone 18:09, 18 March 2007 (UTC)[reply]

Delete (nominator's vote). Datapoint: More than two-thirds of the Google hits for "cwatset" also contain "wikipedia".[2][3]

This AfD nomination was incomplete. It is listed now. DumbBOT 12:58, 19 March 2007 (UTC)[reply]

Delete as copyright violation. Keep, having a second look, it appears not to be just a copy/paste. --Cpt. Morgan (Reinoutr) 14:17, 19 March 2007 (UTC)[reply]
Comment. The article is neither nonsense nor unintelligible. The addition is done bitwise (so, 011+001=010, 110+110=000, 110+101=011, etc.) You can call this XOR if you prefer. A subset C of the set of n-bit words is then a cwatset if for each of its members c, there is some permutation π on the bit positions such that π(c+C)=C. For the example given in the article of a cwatset, C={000,110,101}, we may pick c to be the member 110 of C. We then have

c+C={110+000,110+110,110+101}={110,000,011}

and π should be chosen to interchange the first and second bits and leave the third bit alone:

π(c+C)={π(110),π(000),π(011)}={110,000,101}=C.

As for the relation between groups and cwatsets, the set of all n-bit words under bitwise addition (or XOR) is itself a group. If a subset C of this set is a group under bitwise addition, it will also be a cwatset as we may take π to always be the identity permutation. The converse is not true—{000,110,101} is a cwatset but not a group under bitwise addition. Spacepotato 08:38, 20 March 2007 (UTC)[reply]

Delete. Without a reliable source, this is original research. Gandalf61 09:49, 20 March 2007 (UTC) Withdraw my vote, as article now has published sources. Gandalf61 10:07, 21 March 2007 (UTC)[reply]
Comment. I agree with Spacepotato that the article is not nonsense (though it was badly written). I tried to improve the article because I was too lazy after researching the topic to write down exactly what I think about deleting or keeping the article. For me, this one is really borderline: there are sources out there but it seems to be a really obscure part of mathematics that has drawn very little interest in the mathematical community, and I doubt whether there are enough sources. Together with closure with a twist and GC-set, it forms a cluster of three articles with no incoming links. -- Jitse Niesen (talk) 13:01, 20 March 2007 (UTC)[reply]
Comment. I have added some references to the article. Although there hasn't been much work on this subject, there seem to be sufficient sources for an article. I recommend a keep for this reason. (~~As the nomination appears to have been based on a misreading of the article, I would move for a speedy keep, but that appears to be procedurally impossible at this point.~~) Spacepotato 04:06, 21 March 2007 (UTC)[reply]

Comment. As the nomination looks to have been made in good faith, I'm withdrawing my hypothetical remark regarding a speedy keep as inappropriate. Spacepotato 09:29, 21 March 2007 (UTC)[reply]

Merge into wreath product, or delete. I agree with Jitse's evaluation of the facts. Septentrionalis PMAnderson 14:00, 22 March 2007 (UTC)[reply]
Merge into closure with a twist, and also merge GC-set into the same place. The new references seem to me (barely) enough for notability, but we don't need three articles on the same obscure topic, and we don't need to clutter the more important article on wreath products with this stuff. If we're to keep one of the three titles, closure with a twist sounds best of the three to keep to me. —David Eppstein 07:20, 23 March 2007 (UTC)[reply]
Keep - merge and redirect would be fine, too, but this paper (not exactly a paper, but...) seems to imply that a nice little history and applications section could be added, which makes the concept feel encyclopedic to me. Smmurphy^(Talk) 03:16, 25 March 2007 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.