Linkage

Christian LawsonPerfect collects images of binary numbers in unexpected places after seeing a car with plate number ending in 10110. My contribution to the thread was a Tshirt drawer:

Dan Arena of Vanderbilt ran ChatGPT on his algorithms coursework, and incorporated the results into his weekly lecture material (\(\mathbb{M}\)). As he describes, it did well enough to scare the students, but not well enough to impress the instructor.

2d particlemesh gravity simulation by Ricky Reusser, quickly clumping up to form the sort of netlike distribution of matter that we think the universe should have.

New diamondmodel openaccess journal Innovations in Graph Theory (\(\mathbb{M}\), via), with an impressive editorial board.

Canadian mathematicians Stephanie van Willigenburg, Angèle Foley, and Samantha Dahlberg win the 2023 David P. Robbins Prize of the MAA (\(\mathbb{M}\)) for finding infinitely many nonclawcontractible and clawfree graphs whose chromatic symmetric functions are not positive linear combinations of elementary symmetric functions, disproving a 1995 conjecture of Richard Stanley. One of their classes of examples is very simple: pair off vertices in two triangles and connect the three pairs by three equallength paths.

My cat thinks that the poster tube I just picked up, with newlyprinted poster inside it, makes a great cat toy (\(\mathbb{M}\)). It rolls around when you hit it, and you can bearhug it and then start clawing at it with hind feet. Fortunately the tube is tough but I need to put it somewhere out of reach where it’s less likely to be destroyed. In related posterprinting news: you can just put up a poster at an academic conference and nobody will stop you.

Progress on Heilbronn’s triangle problem (\(\mathbb{M}\)). This is the problem of placing points in a square to maximize the minimum area of any triangle formed by three of them. One can place points so that this area is a little bigger than \(1/n^2\) (by a nonconstant but small amount), and now the best upper bound is a little smaller than \(1/n^{8/7}\). The improvement is the “a little smaller than” term, a polynomial with a tiny exponent. See also Wikipedia and the original preprint by Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov.

Nature on using leftover framing text to catch papers that were written with the assistance of AI text generation (ChatGPT) but not acknowledged to have been (\(\mathbb{M}\), via). Their lead example is in mathematical physics. Some journals allow this sort of use, but only with an acknowledgement. The tools discussed for catching these will only catch sloppy authors who didn’t clean up after their uses, “only the tip of the iceberg”. Also in Nature: generation of fake references by AI tools is becoming less prevalent but still problematic.

Starburst almostHamiltonianpath puzzle. The underlying graph is just the thetagraph \(\Theta(5,2,2)\), so although finding long paths is hard in general, the difficulty here is more from the tangled graph drawing that is given in the puzzle.

Huge number of new solutions to the “freefall 3body problem” (\(\mathbb{M}\)): “Threebody periodic collisionless equalmass freefall orbits revisited”, Ivan Hristov, Radoslava Hristova, Veljko Dmitrašinović, Kiyotaka Tanikawa, arXiv:2308.16159. These are periodic motions for three equal masses under Newtonian gravity. The “freefall” condition means that the motion starts with all three objects at rest (and then repeats that same rest position infinitely often). Therefore, the only information one needs to specify the initial conditions is a triangle, the relative positions of the three bodies at rest. Most triangles will produce chaotic orbits that eventually eject one of the three bodies from the system, but some special triangles lead to periodicity. There were many periodic solutions to the 3body problem known previously, but only a much smaller number for this freefall variation. Found via ACM TechNews pointing me to a popularpress summary in New Scientist that I’m not going to link because it appears to be irredeemably paywalled.

Unit strips of length shorter than \(\sqrt{3}\) cannot form a smooth Möbius strip (\(\mathbb{M}\)), solving a 50yearold open problem. See also Richard Schwartz’s preprint “The optimal paper Moebius band”, arXiv:2308.12641.

DDoS attack on ArXiv (\(\mathbb{M}\)), coming from somewhere in China, for unexplained reasons.

The arXiv version of the full proceedings for Graph Drawing 2023 is now online (\(\mathbb{M}\)), as it has been for previous years. The more official proceedings will be published later by Springer LNCS, differing in a couple of ways: First, the arXiv versions can include appendices but the LNCS versions do not. And second, the LNCS version has (at least in the past) also included a section of poster abstracts (limited to two pages, not counting appendices) that are not in the arXiv proceedings. The conference itself takes place next week in Palermo.