Linkage

El poema de los números primos (\(\mathbb{M}\)). Exhibit of the mathematicallyinspired artworks of Esther Ferrer, at Tabakalera in San Sebastián, Spain.

How combinatorics became legitimate (\(\mathbb{M}\)). Igor Pak recommends two interesting video interviews with László Lovász and Endre Szemerédi. The whole interviews are quite long but they’re broken into 10minute clips and Igor has picked out the ones relevant to the title.

Magic angles and superconductivity in twisted graphene (\(\mathbb{M}\)). If you twist two sheets of hexagonally tiled carbon relative to each other you can get a superconductor, but only for certain very specific twist angles.

Matthew Butterick says no to ligatures in programming fonts (\(\mathbb{M}\), via). I tend to agree. They make some things cuter but more things inconsistent. The lack of a short double back arrow in the Fira example is telling. And anyone who expects to see individual characters has to know what font they’re displayed in and how it mangles them to understand what they’re reading. But if you like these for your own text editing, whatever. Just show me the ASCII when I have to view it in my browser.

Breaking the Bellman–Ford shortestpath bound (\(\mathbb{M}\)). Amr Elmasry claims a time bound of \(O(m\sqrt{n})\) for singlesource shortest paths in graphs that may have cycles and negative edge weights, but no negative cycles. If correct, this would be a big improvement over the \(O(mn)\) time for Bellman–Ford. However, I got stuck somewhere around Lemma 3 when trying to understand it. Anyone else have better progress?

Some actual data on how the subject’s gender influences biography creation and deletion on Wikipedia (\(\mathbb{M}\)). Stillexisting older articles on women are more likely to have gone through a deletion discussion than men, but we don’t know whether more were nominated or equally many nominated but women survived better, and whether the inequality of nominations has lessened recently or the greater nomination rate for women takes longer to kick in and is still prevalent.

The graphs behind Reuleaux polyhedra (\(\mathbb{M}\)), by Luis Montejano, Eric Pauli, Miguel Raggi, and Edgardo RoldánPensado. These shapes are the intersections of equalradius balls centered at their vertices; smoothing some edges gives them constant width. Their vertices are the finite point sets with the most diameters. Their vertexedge graphs are selfdual, unlike other polyhedral graphs. And their vertexdiameter graphs are 4colorable. Examples include pyramids over odd polygons.

It’s not like it’s difficult to make your own out of, you know, paper, but if you want a colorful kit to teach yourself about the Miuraori and three other folds, this one looks pretty if a little overpriced at $20 for eight sheets of paper (\(\mathbb{M}\)).

Tensor products of graphs can require fewer colors than their factors (\(\mathbb{M}\)). This short new preprint by Yaroslav Shitov gives counterexamples to Hedetniemi’s conjecture from 1966. In a new blog post Gil Kalai explains the construction.

Algorithms and natural history (\(\mathbb{M}\)). In a new blog, Laurent Feuilloley writes about some algorithmic problems on polyhedra coming from the measurement of skulls, diamond cutting, and the use of symmetry to undo deformations of fossils.

Did you know that Swiss mathematician Alice Roth invented Swiss cheese? (\(\mathbb{M}\)). A Swiss cheese is a disk with smaller disks removed, leaving no interior. Scientific American alerted me to this amusing terminology but I got a clearer idea what they’re good for from an exercise using them to show complex conjugation to be wellbehaved on a compact domain but hard to approximate by rational functions.

China is now blocking all language editions of Wikipedia (\(\mathbb{M}\), via), expanding its previous block which applied only to the Mandarin edition.
Of course their internet blockage is hardly the biggest problem with China these days. I was surprised to find that some of my usuallywellinformed friends hadn’t even heard of “the largest mass incarceration of the 21st century” and “precursors to genocide”, China’s concentration camps for up to a million Uighur people. So read and learn.

Hazel Perfect (\(\mathbb{M}\)). A new Wikipedia article on the inventor of gammoids (how I came across her name this time) and Christian LawsonPerfect’s mathematical hero (despite or because of the unexplained similarity of names).

In a recent poll, “56% of Americans said Arabic numerals should not be taught in American schools” (\(\mathbb{M}\)).