Linkage

Lattice path matroids (\(\mathbb{M}\)). An interesting generalization of the uniform matroids with which I was previously unfamiliar. They are defined by two monotone lattice paths in a rectangular grid, one below the other. The bases are lattice paths between the two defining paths, described by the set of positions at which they step upwards.

My university is threatening impending doom for course materials or online content that does not pass some unspecified accessibility check. All my course materials are formatted in LaTeX/beamer. If accessibility is defined as “images have alt text”, then I know how to define alt text as a parameter to the includegraphics macro, but I strongly suspect it is getting dropped on the floor rather than included in the generated pdf. If accessibility is defined as “passes all Acrobat accessibility checks” then I am even more at sea.

I do want my materials to be accessible but I have done little about this so far because without further guidance this seems an impossible demand, like that I suddenly rewrite all my content in a foreign language that I have not studied. And I have no expectation that my campus accessibility people will or can provide any help. In the linked discussion thread I asked for advice on producing accessible documents with pdflatex and beamer, in a way that maintains interoperability with all the external systems I need to use that also use LaTeX. Nobody was able to suggest anything that could produce accessible pdfs this way; it does seem possible to produce pdf side-by-side with accessible html.

One useful-looking response from Jannis Harder pointed to an explainer from the National Center on Accessible Educational Materials and quoted ADA Title II rules stating that in cases where technical limitations prevent making content directly accessible (seemingly true for pdflatex) conforming alternative versions (possibly in html) may be acceptable. But as of posting here my university’s accessibility office has not responded to my two-week-old request for information on whether they would consider side-by-side html to be acceptable as a way of providing accessibility.

The Tromino Puzzle (\(\mathbb{M}\)), 85 laser-cut wooden trominos to be fitted into a \(16\times 16\) square with an arbitrary square missing, with the proof that this is always possible providing an interesting exercise in induction proofs that aren’t just sum or product formulas.

The Mathematics of Origami (\(\mathbb{M}\)), new book by Joe O’Rourke coming out this December from Cambridge University Press.

Niles Johnson’s 11-year-old adds commentary to a blackboard calculation involving mod-2 binomial coefficients.

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra (\(\mathbb{M}\)), a 2009 Nature paper by Amir Haji-Akbari et al., with interesting figures of dense packings involving cylindrical rods of spiraling tetrahedra packed together with more tetrahedra filling the gaps.

Hand-drawn talk slides by Nathan Harms (\(\mathbb{M}\)). Harms was a fine arts student before becoming a theoretical computer scientist and it shows.

Christian Lawson-Perfect collects pre-1950 examples of color figures in mathematics publications.

Mumford’s conjecture on stable mapping class groups was supposedly proven in 2007 by Madsen and Weiss (\(\mathbb{M}\)), but the lack of justification for its assertion that all smooth triangulations can be blurred casts it into doubt. Here a blurring is a smooth homotopy that pushes points near the boundary of each simplex onto the boundary, so that each simplex has a neighborhood that is mapped onto the simplex. Doing this continuously simplex by simplex is easy enough but keeping it smooth is a problem.

Quanta on the smoothness of high-dimensional minimal surfaces (\(\mathbb{M}\)). Below eight dimensions they behave nicely but then weird behavior might emerge. New results show that generic minimal surfaces stay nonsingular for at least three more dimensions.

A Quasi-Polynomial Time Algorithm for 3-Coloring Circle Graphs (\(\mathbb{M}\)), E. S. Ajaykrishnan, Robert Ganian, Daniel Lokshtanov, and Vaishali Surianarayanan. New preprint, awarded best paper at the SIAM Symposium on Simplicity in Algorithms to be held next January in Vancouver. Does what it says in the title, solving a problem left unresolved after work in the early 1990s claimed to find a polynomial time algorithm but without detail and with methods later shown not to work.

Clarivate puts mathematics back onto its Highly Cited Researchers list (\(\mathbb{M}\)), after removing it in 2023 for being too heavily gamed. They say they’re incorporating more safeguards against abuse, but I’m not convinced that this is any better of an idea than it was the first time around. There are good researchers in the list but, even setting aside the differences between importance, influence, and citability, you’ll still find the same old issues of the list being unrepresentative of mainstream mathematics, with its balance of topics too much dominated by prominent researchers in mathematics-adjacent fields that are more heavily cited, and with too much credit given to subfields of mathematics that are overrun by dubious-quality cite-farm publications (fuzzy fractional differential equations, etc).

Article from Inria giving a behind-the-scenes look at the open-access journal TheoretiCS (\(\mathbb{M}\)).