Chris Purcell @ccppurcell@mathstodon.xyz

When n=2k-1 the graph is isomorphic to the Kneser graph \(KG_{n,n-k}\) ..but I am still interested in the general case

Anyone know the name of the class of graphs on \({n \choose k}\) vertices, each vertex is a \(k\) element subset of \(\{1,\ldots,n\}\) and there is an edge \(ST\) if and only if the intersection of \(S\) and \(T\) is a singleton? When n=5 k=3 you get the Petersen graph for instance. In fact I am interested in the case n=2k-1 anyway...

I guess \(C_3^0\) is not the right notation, because then you would have three loops. On the board, I wrote \(C_3^\emptyset\) which is better

Came across a nice sequence of graphs that should have a nice name, or a better description than I have been able to come up with. Using the notation in the wikipedia page for circulant graph https://en.wikipedia.org/wiki/Circulant_graph
So for example \(C_7^{1,2}\) is the graph on {0,1,2,3,4,5,6} with an edge uv if and only if u-v is in {1,2,-1,-2} mod 7. The sequence is like this
\(C_3^0,C_4^2,C_5^1,C_6^{1,3},C_7^{1,2},C_8^{1,2,4},C_9^{1,2,3}\ldots\)
See the graphs labelled 3...9 (ignore the other doodles)

"In the new commission the areas of education and research are [...] subsumed under the "innovation and youth" title. This emphasizes economic exploitability (i.e. "innovation") over its foundation, which is education and research, and it reduces “education” to “youth” while being essential to all ages...

With this open letter we demand that the EU commission revises the title for commissioner Gabriel to “Education, Research, Innovation and Youth”"

https://www.futureofresearch.eu/

I think (correct me if I am wrong) that google is trying to guess what I might want to know based on data about me, based on what similar people who made similar searches eventually clicked on, etc. etc. rather than the pure output of a pagerank type algorithm. But that's very annoying because I have some specific question that a general audience wouldn't necessarily think to ask.

Google kind of sucks. I am curious about how close to the speed of light we can get (in a spaceship for instance). We're not even close to 0.01c as things stand, but I have many questions: are there engineering reasons to believe we will/won't get to p*c for any p? What tech is being proposed/ruled out etc. no matter what I search, google shows me things like "why can't we/what would happen if we go faster than light?" and all sorts of intro stuff that I already know.

In recent years I have mainly reviewed for CS conferences. Now I am reviewing a paper for a mathematics journal and they're asking for a rating out of 100... how can you possibly boil down a scientific paper to a number out of 100? It seems absurd to me. I don't remember doing it in the past (but my memory for such things is bad)

There are two types of mathematician in the world: those who like to include the current year in their exercises/examples/puzzles and those who don't.

If a mathematician is a machine for turning coffee into theorems, what is the relationship between the quality of the coffee and the quality of the theorems? Is bad coffee at conferences a false economy?

Evidence that Swedish people are very polite: the word "borg" is pronounced "bori" and yet several people I know of who work closely with someone named x+"borg" (or for example spent their careers commentating on Björn Borg) consistently mispronounce it.

In mathematics talks, a theorem will be given with a list of its authors (on the slides). When the speaker is one of those authors, they are commonly listed only by the initials of their last names. I want to know: why is this, and when did this start?

I realise now that the way I have been saying this fact is very ambiguous (I can make it make sense with tone of voice and hand gestures).

I mean to say there is exactly one number that is the successor of a square and whose successor is a cube, or to put it another way, there is exactly one solution to y³-x²=2 with x,y integers.

I learned this fact in a very Ramanujan-esque fashion, as a friend turned 26 and suggested on facebook that it wasn't a particularly interesting number - another friend commented to the contrary, that it was a very interesting number for the given reason. In writing these toots, I learned another fact (that I suspected but somehow never thought to check) that indeed y³-x²=k for k ∈ ℤ has only finitely many integer solutions.
3/n

Surely the gaps just grow larger and larger? And surely once you establish that there is no counterexample in the first thousand numbers or so, we can just go home? Which led us on to a nice discussion of the prime-counting function π(n) and the logarithmic integral li(n) and the fact that li(n)-π(n) is positive for very many values (it switches around n=10³¹⁶ according to wikipedia) but turns out to switch signs infinitely often. Well that's my outreach for the week! 2/n

Over the weekend I was canoeing and one of my companions (in another boat) asked me for a maths fact as we paddled along. Many parameters to consider here (background, attention span, lack of blackboard) and I went for: there is exactly one number between a square and a cube. It turned out to be a good choice! The instinctive response was "it must be a small number" - good instinct in my opinion. But then I mentioned that it is not exactly trivial to prove and an objection was raised 1/n

for x,y,z,n ∈ ℕ, both

xⁿ+yⁿ=zⁿ and

nˣ+nʸ=nᶻ

have infinitely many solutions when n=2 and no solutions when n>2 :)

It's so easy to spend fifteen minutes doing nothing important, but very hard to spend fifteen minutes doing nothing.

There are (at least) two (apparently) unrelated classes of graphs called "parity graphs". One is the class of graphs in which the size of a maximal independent set is fixed mod 2. The other is the class in which the length of an induced u-v-path is fixed mod 2 for all pairs of vertices u,v. By coincidence, both are somewhat connected to research projects of mine, but the overloaded terminology is annoying.