Earlier this year there was a conference in Budapest, Hungary, named Sum(m)it280, to honor the cumulative 280th birthday of the Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach. There the organizers asked participants for survey articles for a conference volume on extremal problems in combinatorics and geometry. Now I have worked a reasonably amount […]
One of the greatest discovery of in the theory of distance-regular graphs has been the twisted Grassmann graph by Edwin van Dam and Jack Koolen. Here I want to describe a small variation of their construction for the twisted $ {D_{5,5}(q)}$ graph. This post mostly to preserve my blackboard on the topic. (I tend to […]
A few days ago China celebrated one of many Chinese Valentine’s days: the 20th of May. Why is this a special day in China? Chinese has around 30 to 36 phonemes which is plenty, but Chinese phonotactics dictate that you can only make around 1200 syllables out of them, for instance, see this video. English […]
This week I put two new preprint on the arXiv. Both are on a similar theme, so I will discuss them together. One is with Morgan Rodgers on regular sets of lines in rank 3 polar spaces. The other one is solves a problem which I have been thinking about very regularly since November 2017: […]
Last week I had a cold and could not do much thinking. So I spent my time making TikZ pictures for an upcoming talk of mine. This talk is on my recent work with Akihiro Munemasa on constructing cospectral strongly regular graphs. I think that the pictures are nice for a blog post, so here […]
Permutation Groups, Analysis of Boolean Functions, Finite Geometry, Coding Theory and Algebraic Graph Theory Important mathematical concepts get reinvented many times. In my recent work with Yuval Filmus we explored objects that are called (in random ordering) Boolean degree 1 functions, Cameron-Liebler line classes, equitable partitions, completely regular strength 0 codes with covering radius 1, […]
This year is László Lovász‘s 70th birthday and I went to his birthday conference, so a blog post about one of his famous results seems to be appropriate: the chromatic number of the Kneser graph. Let $ \Gamma$ be a graph with a vertex set $ V$ and an adjacency relation $ \sim$. A coloring […]
Today’s topic combines three of my favorite subjects: Erdős-Ko-Rado theorems (EKR theorems), finite buildings and spectral techniques. All of these topics deserve their own books (and have them, here some examples which I read: Erdos-Ko-Rado Theorems: Algebraic Approaches by Chris Godsil and Karen Meagher, Spectra of Graphs by Andries E. Brouwer and Willem H. Haemers, The Structure of Spherical […]