(This challenge exists to extend sequence A276272 in the On-Line Encyclopedia of Integer Sequences, and perhaps create a new OEIS sequence1.) This is a code-challenge, which will have you write code to compute as many terms of this sequence as possible. --- Background A polytet is a kind of polyform which is constructed by gluing regular tetrahedra together face-to-face in such a way that none of the interiors of the tetrahedra overlap. These are counted up to rotation in 3-space but not refl...| Recent Questions - Code Golf Stack Exchange
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
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
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
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
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
