The 28th edition of the Buildings conference is held in Ghent (where I am currently based) this September. [Note that this is unrelated to the actually buildings which you live and work in. The mathematical branch of building theory is abstract algebra. I have one post mentioning them.] Now I am not in the habit of announcing conferences here, so why this post? (It isn’t a good reason.) I just had a look at the list of invited speakers on the conference homepage (accessed on 24 August 2022, 22:04, Belgian time):
Only one “tba”. For the University of Bielefeld. Among all “silly” conspiracy theories, the Bielefeld conspiracy (in short: Bielefeld does not exist) might be the most popular one: Tom Scott made a video about it, Angela Merkel referenced it in a speech, people, who claim to be from Bielefeld, regularly express their frustration with it, and some people claim that it is no longer funny. (But it is a German joke, so maybe it never was funny.) Anyway: the “tba” should not surprise anyone.
Today I write about a recent hobby of mine: Collecting strongly regular graphs. It started three years ago. You can find my collection on my homepage. I collect many SRGs with known parameters. It started here. This is about size, not quantity, and tries to give an idea how a typical SRG with certain parameters might look like. By now my collection has grown so big that I should advertise and describe it.
At the time of writing, my collections splits into four parts. The first two parts are graphs generated with GM- or WQH-switching. The second two parts are graphs generated with what I call Kantor switching. All the data is provided in graph6 format in a compressed text file. In total something beyond 190 million.
Recently, while working on a research project, I got on a tangent. From this tangent, I got on another tangent and that is what I want to write about today: a very nice Boolean function. This example got rediscovered several times for different reasons and, as I try to emphasize from time, I believe that things that are getting rediscovered many times must be of particular importance.
So let us define our Boolean function. I will give three very similar definitions throughout this post, but I will start with only one. Put . Our Boolean function is defined as follows: Put (as ). For , write as with and . Then use this rule:
- If , then .
- If , then .
- If , then .
- If , then .
In the following, we list some properties of this function. Many of the concepts here are also discussed in an earlier post of mine.
Germany votes for a new parliament on the 26th of September 2021, so only in a few weeks from now. What do the German parties say about math in their election platforms? Not much, but they talk much about math-related topics such as artificial intelligence and quantum computing. So let us have a look! Actually, only at quantum thingies. Otherwise, it is too much to write here.
Hoffman’s bound (or: ratio bound) on the size of a coclique (or: independent set, stable set) in a graph is one of the most important bounds in spectral graph theory. At the same time it is often misattributed. Primary reason for is that Hoffman never published it, but people want to cite something for it. A few weeks ago, Willem Haemers published a nice article which presents the history of Hoffman’s ratio bound (here is the journal version).
As I have probably misattributed the bound myself in the past and even one of my favorite books, “Distance-Regular Graphs” by Brouwer, Cohen and Neumaier does so too (but they correct it online), I wanted to make this quick post.
The sad occasion of Willem’s article is that Alan J. Hoffman past away on the 18th January 2021 at the age of 96. May he rest in peace.
One of the structures investigated in finite geometry are related to quadratic forms over finite fields (see below for definitions). Knowledge on the geometry of singular points of quadratic forms is very common and covered in many textbooks on finite geometry, but one cannot say the same for the geometry on non-singular points. This short post tries to amend this a little.
(This is no surprise as the geometry with singular points is much nicer than the geometry associated with various types of non-singular points. Also, everything in the following is well-known for decades. It is simply a bit more obscure than other facts about finite quadrics. Lastly, my title is a terrible pun on slang from the mid-20th century (and Pulp Fiction).)
When you submit an article in mathematics to a journal, then it will be reviewed by other mathematicians. These are unknown to you. It is a so-called single-blind process. This is so that the referees do not have to fear the wreath of the authors if they write a bad review. Now often this anonymity is a bit of a lie. You might know the style of a referee and recognize her that way. Sometimes the referee intentionally reveals herself for a variety of reasons (more commonly, after the article is published). But for me, the only time when I dare to guess the referee is when she unintentionally reveals herself. Namely, by PDF metadata. This is a short note on how to avoid this case as a reviewer.
Often, when you write your referee report, your LaTeX compiler will add some meta-data. This metadata can be used to de-anonymize a referee report. Now I do not want to get into examples, but you can see the metadata in your PDF file usually under “Properties” in your PDF reader.
Here now a quick guide to avoid this reliably. My example is for Linux, but Windows or Mac users have the same tools available to them. That is, you need exiftool and qpdf. If the name of your referee report is
review.pdf, then you can do the following in your console/shell (in the same directory as
exiftool -all= -overwrite_original review.pdf
$ mv review.pdf tmp.pdf
$ qpdf --linearize tmp.pdf review.pdf
Note that for Windows “mv” is “move”. Now your referee report is free of metadata and it is harder for the author to guess who you are. Besides these technicalities, always pay attention to metadata when at least a superficial level anonymity is important.
A quick post about small Ramsey numbers. I like to write on my blog about things which I do not intend to publish, but also do not want to keep as private knowledge. This is one of these posts.
Stanisław P. Radziszowski writes the following in the 15th revision of his survey on small Ramsey numbers:
One can expect that the lower bounds in Table II are weaker than those in Table I, especially smaller ones, in the sense that some of them should not be that hard to improve, in contrast to the bounds in Table I.
Table II contains slightly larger Ramsey numbers, for instance and . So when one has idle CPU time, it seems to be reasonable to use it here, I thought some weeks ago. And indeed, it is. I found a witness for and a witness for for . This improves the previously known lower bounds by a gigantic 7 in the first case and a nearly as gigantic 6 in the second case. Here you can find a short description of both cases.
And if anyone asks: The upper bounds are much, much, much larger than both lower bounds. Also I did not put any effort into my search, so it is probably very feasible to improve a few more numbers in Table II of the survey.