Chris Purcell @ccppurcell@mathstodon.xyz

Could be a good puzzle either to prove, or if I am wrong to find a counter example.

Oh and probably n should be at least 3. So far I've mainly played games where n=3

I've been playing "binary sudoku". You have a 2nx2n grid, with some 0s and 1s and you have to fill it in according to some rules:
* each row and column has equal number of 0s and 1s
* no row or column has a run of three 0s or 1s
* no pair of rows is the same
* no pair of columns is the same

conjecture: there must be a pair of rows (or columns) that are "inverse" i.e. a pair of strings s t where s[i]=/=t[i] for all i.

I can see a boring case analysis proof but is there an "at a glance" proof?

Has anyone here ever seen, in a paper or book that covers boolean satisfiability, a neat way to refer to the "sign" of a variable appearing in a clause, in such a way that I could take the product of two signs (with several variables appearing positively and negatively perhaps in the same expresssion). I am tying myself in notational knots here. I have previously sometimes used \(x^\alpha\) and α should be -1 or 1. But that gets messy if you have multiple clauses and variables

Perhaps "class" is a better word than category...

I'm sure many of you have seen this, it's a couple of years old - there's a sort of lattice of quadrilaterals (a square is a rectangle is a parallelogram etc) but it's a bit ugly if you stick to standard named ones. Here a "kitoid" is introduced to make a really beautiful diagram

https://www.hambrecht.ch/blog/2017/7/26/the-quest-for-the-lost-quadrilateral

But it got me thinking, is there any well defined sense in which these categories are exhaustive (for convex quads)? And if so how many are there for n-gons

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