Dror Bar-Natan (homepage, Wikipedia) told me about his work with Roland Van der Veen (homepage, arXiv, YouTube) on a wonderful knot invariant which distinguishes knots much better than other knot invariants, and can be computed quickly even for knots of … Continue reading →| Combinatorics and more
Polynomial bounds for the Chowla cosine problem were achieved independently in two very recent works. Zhihan Jin, Aleksa Milojević, István Tomon, Shengtong Zhang: From small eigenvalues to large cu…| Combinatorics and more
My previous post was about an asymptotic solution of Rota’s basis conjecture and the next few posts will also be devoted to some mathematical news. Before moving to the main featured result let me mention a beautiful blog post by … Continue reading →| Combinatorics and more
Richard Montgomery and Lisa Sauermann: Asymptotically-tight packing and covering with transversal bases in Rota’s basis conjecture Abstract: In 1989, Rota conjectured that, given any bases of a vector space of dimension , or more generally a matroid of rank , … Continue reading →| Combinatorics and more
Toufic Mansour The fourth International Conference on Enumerative Combinatorics and Applications will take place online, August 25–27, 2025. As in the previous three editions, the conference opens …| Combinatorics and more
Nine years ago, I wrote a July 4th blog post about matroids called A Celebration of Independence. Today, I’d like to talk about independence’s lesser-known sibling. In particular, I want to describe a characterization of matroids due to Paul Vaderlind that I feel ought to be better known. In most books and articles on matroid […]| Matt Baker's Math Blog
Congratulations to all of the winners of the 2022 Fields Medal! The only one I know personally, and whose work I have studied in detail, is June Huh. I’m happy both for June himself and for the field of combinatorics more broadly, which at one point was not taken seriously enough by the mathematics community […]| Matt Baker's Math Blog
In this post I will provide a gentle introduction to the theory of martingales (also called “fair games”) by way of a beautiful proof, due to Johan Wästlund, that there are precisely labeled trees on vertices. Apertif: a true story In my early twenties, I appeared on the TV show Jeopardy! That’s not what this […]| Matt Baker's Math Blog
(This is a guest post by Bhavik Mehta) On March 16, 2023, a paper by Campos, Griffiths, Morris, and Sahasrabudhe appeared on the arXiv, announcing an exponential improvement to the upper bound on Ramsey numbers, an open problem since 1935. … Continue reading →| Xena
Recently, I got an IKEA LILLABO train set for my daughter. It has twelve curved segments, each is 1/8th of a circle of radius 1, two straight segments of length 1, and a bridge of length 2 (in top ...| Puzzling Stack Exchange
h/t Benny Sudakov The Ramsey number R(ℓ,k) is the smallest integer n such that in any two-coloring of the edges of the complete graph on n vertices, , by red and blue, there is either a red (a complete graph … Continue reading →| Combinatorics and more
Joram’s seminar 2025 Here is my summary of the recent Joram’s seminar that took place on July 9 and 10 in Jerusalem. Much of the seminar was about the the paper Product Mixing in Compac…| Combinatorics and more
Here's an interesting question: given a target integer n,| mathesis
You can define a rooted planar binary tree recursively by this equation:| golem.ph.utexas.edu
Let me briefly report on two birthday conferences for long-time friends and colleagues Saharon Shelah and Yuri Gurevich. Yuri fest took place in Munich and on Zoom between June 20–22 2025 and Shelah’s birthday conference will be held in Vienna … Continue reading →| Combinatorics and more
First lecture in a 4.5-hour minicourse on combinatorics with species.| The n-Category Café
Second lecture in a 4.5-hour minicourse on combinatorics with species.| The n-Category Café
Species and their generating functions| golem.ph.utexas.edu
Is there anything new in Enumerative Combinatorics? Most experts would tell you about some interesting new theorems, beautiful bijections, advanced techniques, connections to other areas, etc. Most…| Igor Pak's blog
Update: Let me mention a ninth paper that just appeared on the arXive. IX. … and the optimal sofa for the moving sofa problem is … Gerver’s sofa. Optimality of Gerver’s Sofa…| Combinatorics and more
It is commonly advised that dictionary words should not be used when forming passwords. We would like to make the case that dictionary words can be used as long as the words are randomly chosen. Th…| All Math Considered
It is commonplace for frequent users of the Internet to have multiple online accounts that require passwords. Advice and guidelines abound on the Internet on picking safe and strong passwords. They…| All Math Considered
This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of pro…| All Math Considered
This is the fourth post in a series of posts on combinatorial analysis. The post is opened with the following problem. This post builds on the previous post on binomial coefficients. Figure 1 ̵…| All Math Considered
This is the third post in a series of posts on combinatorial analysis. The post is opened with the following problem. Figure 1 Path Problem Point Q is 7 blocks east and 6 blocks north of Point P (s…| All Math Considered
I am on record of liking the status quo of math publishing. It’s very far from ideal as I repeatedly discuss on this blog, see e.g. my posts on the elitism, the invited issues, the non-free a…| Igor Pak's blog
Starting a paper is easy. That is, if you don’t care for the marketing, don’t want to be memorable, and just want to get on with the story and quickly communicate what you have proved. …| Igor Pak's blog
