Linkage

Brick territories experiment (\(\mathbb{M}\)). What shapes do you get when (n) simultaneous breakout games compete against each other for pixels?

Lillian Oppenheimer, 1898–1992 (\(\mathbb{M}\)), early and significant promoter of origami in the US, founder of the organization that became OrigamiUSA, mother of notable mathematicians William Kruskal, Martin David Kruskal, and Joseph Kruskal, and grandmother of computer scientist Clyde Kruskal. Now a Good Article on Wikipedia (not one that I wrote or edited; I merely reviewed it).

Python sets and dictionaries can have quadratic-time performance (\(\mathbb{M}\)), for adversarially-chosen data.

Terry Tao on what can be learned from studying problems rather than on what their solutions happen to be.

Ig Nobel Prize goes to a study showing that rich people are more likely than others to steal candy from children (\(\mathbb{M}\)). The recipient, Paul Piff, is a social psychologist at UC Irvine.

Three dimensional dominoes (\(\mathbb{M}\)), in the same sense as the three-dimensional matching problem rather than in the geometric sense one might conventionally expect.

Zoom now stays alive in the background and reads everything written to the Linux/X11 clipboard. As one commenter writes, “It would be interesting to know what Zoom actually does with the captured clipboard content.” It might not actually be malware.

Tadashi Tokieda gave a beautiful invited presentation at JCDCG\(^3\) on the mathematics of folded and crumpled paper (\(\mathbb{M}\)). In it, he complained about the various poor choices of notation people have used for the Poisson ratio (https:// en.wikipedia.org/wiki/Poisson%27s_ratio), and proposed instead the notation \(\mathop{\rlap{\hspace{0.12em}\cdot}{\alpha}}\) (an alpha with a dot inside it, which I have coded here as \mathop{\rlap{\hspace{0.12em}\cdot}{\alpha}}). Half of the audience (the ones who spoke any French) broke out laughing but he left the joke unexplained.

Slides for my talk at JCDCG\(^3\), “Patterns of Tangent Spheres” (\(\mathbb{M}\)).

There’s so much going on at once in the LLM/mathematics world and so many people providing insightful comment on it that I’m not even going to try to add to it (\(\mathbb{M}\)). Instead, here’s a nice recent preprint where “all original results, proof strategies, and mathematical content predate the use of AI assistance” despite some AI use in cleaning up the writeup: “Forbidden subgraphs of graphs with low bandwidth”, by Maria Chudnovsky, Daniel Lokshtanov, and Eran Nevo. Given any graph \(G\), in fixed-parameter time in a parameter \(k\), they find either a subtree of bandwidth \(\ge k\) or a linear layout of bandwidth \(\le f(k)\) for some (badly exponential) function \(f\). There is additionally a structure theorem describing the high-bandwidth subtrees as having a special form (high pathwidth, or high ratio of vertices to diameter, or a “skewed Cantor comb”.

A topological picture book (\(\mathbb{M}\), via). 3d topological models rendered as “hand-hatched surfaces after the mid-century manner of Francis, Apéry, Hilbert–Cohn-Vossen”. The project creator adds in the via link that it was based on Aaron Hertzmann and Denis Zorin’s “Illustrating smooth surfaces”.

Almost linear universal point sets for planar graphs (\(\mathbb{M}\)). New arXiv preprint by Taylor Gordon. No affiliation listed, but Gordon was a student of Anna Lubiw at Waterloo, and is apparently now at OpenAI.

Analog Library Premium Edition™ (\(\mathbb{M}\)), nice free landing page for any doi.

Peter Luschny laments the now-rapid death of most external links from OEIS.