Category Archives: chatter

Superpermutations: lower bound

I wrote about superpermutations here: a superpermutation is a string that has as substrings all the permutations of some set of symbols. For example, there are six permutations of the symbols 1, 2, 3. They are: 123, 132, 213, 231, … Continue reading

Posted in chatter | 4 Comments

Squares of squares, and the group of rational points on the circle

The purpose of this post is to describe a slightly different way of thinking about the existence – or otherwise – of a 3×3 magic square of squares. Of course it may not lead to any real progress, but it … Continue reading

Posted in chatter, Mathematics | 1 Comment

Almost-magic squares of squares

In the last post we saw that every 3×3 almost-magic square is a rearrangement of three three-term arithmetic progressions that have the same common difference. In other words, if we pick any three numbers x, y and z, and any … Continue reading

Posted in chatter, Mathematics | 2 Comments

Magic squares of squares: Part I

A recent Numberphile video discussed an intriguing unsolved problem in number theory: is there a 3×3 magic square whose entries are all square numbers? (Matt Parker proposed a solution which doesn’t quite work: see the video for more. The “Parker … Continue reading

Posted in chatter, Mathematics | 2 Comments

The UK Government Statistical Service recently released its good practice guidance for releasing statistics in spreadsheets. While this advice is clearly well-intentioned*, and parts of it are good, the overall effect is to encourage the release of data in formats … Continue reading

Posted in chatter, Kiln | 7 Comments

Tackling the Minimal Superpermutation Problem

What’s the shortest string that contains every possible permutation of ABCD somewhere inside it? As it happens, it’s 33 letters long: ABCDABCADBCABDCABACDBACBDACBADCBA. A string like this is called a minimal superpermutation. So what’s the shortest string that contains every possible … Continue reading

Posted in chatter, Mathematics, news | 6 Comments

I hate the Pumping Lemma

I hate the Pumping Lemma for regular languages. It’s a complicated way to express an idea that is fundamentally very simple, and it isn’t even a very good way to prove that a language is not regular. Here it is, … Continue reading

Posted in chatter | 45 Comments

“Venn diagram” partitioning

Paddy3118 wrote about partitioning elements in the same way a Venn diagram does. So, if we have sets A, B and C, the partitions are

Posted in algorithms, chatter | 1 Comment

Linear Logic without Units

My PhD thesis (2007) was available for several years from my web site at the University of Manchester, but since that site was taken down it’s been unavailable. Today’s announcement is that I’ve finally got round to uploading it to GitHub.