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 […]
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 […]
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, […]
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. […]
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 […]
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 […]
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 […]
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 […]
I started writing this blog post some months ago. Occasion was that my paper “A construction for clique-free pseudorandom graphs” (in joint work Anurag Bishnoi and Valentina Pepe) was accepted by Combinatorica with minor revisions. More precisely, one of the referees was unfavorable of publication because he got the impressions that we are simply restating […]
Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36, 10, 4, 2), but there are 32548 non-isomorphic graphs with parameters (36, 15, 6, 6). Peter Cameron, Random Strongly Regular Graphs? This a shorter version of this report which I just […]