Bielefeld Buildings Conspiracy
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 […]
Collecting Strongly Regular Graphs
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 […]
A Boolean Function with Small Degree and Many Variables
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 […]
German Elections! What do the parties say about ̶m̶̶̶a̶̶̶t̶̶̶h̶̶̶?̶ quantum?
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, […]
The History of Hoffman’s (Ratio) Bound
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. […]
Don’t be a Square (but count them)
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 […]
Quick Note: How to Referee Anonymously
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 […]
Almost a Hadamard Matrix
Recently, Yu Hin Au, Nathan Lindzey, and Levent Tunçel published a preprint with various spectral bounds on the arXiv. They investigate generalizations of bounds due to Delsarte and Hoffman in the context of the Lovász-Schrijver SDP. Page 12 of that article I knew for a few more days because Nathan asked me if their bound […]
R(5, 22) and R(6, 21)
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 […]