Chris Purcell @ccppurcell@mathstodon.xyz

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.

I was looking up bad mathematical notation and obviously sin² vs sin⁻¹ came up. I came across a reddit comment that said something like "just use arcsin, problem solved". This is annoying to me because sin⁻¹ is the "correct" notation, it's sin² that is the abomination.

wait the above is wrong, that's just the set of all multisets!

Hm maybe \(S^\mathbb{N}\) works? Each multiset is a function f:S->N where f(s) is the multiplicity of s? ... I don't like it though

Stupid notation question: is there a standard way of expressing "the multisets of size k whose elements are in a set S" or to put it another way the unordered k-tuples, I guess. I want something like Sᵏ

The slope number of a graph G is the minimum number of distinct gradients of the edges in a straight line drawing of G.

An open problem that is very nice in my opinion: When Δ(G)≤3 the slope number of G is at most 4. For any k there is a graph G with Δ(G)=5 and slope number >k. But what about Δ(G)=4?

Not really my area at all but I like questions like this: where's the boundary?

https://en.wikipedia.org/wiki/Slope_number

When I add say 579 and 345, my inner monologue says "eight *nine* one *two* four nine hundred and twenty four!"

#27plus48

Did you know that the diagonals (for a suitable definition of diagonal) of Pascal's triangle add up to the Fibonacci numbers?

The universe sometimes appears to be governed by the most beautiful laws, and physicists even use this as a guiding principle it seems. But I would argue that the best you can hope for is locally maximal beauty.

Whenever I toot something mathematical I have a spike in anxiety that I will have made a stupid mistake! And I spend an inordinate amount of time proof reading such toots.

The other day I was thinking about graphs that have degree sequence 1,3,3,3,... such graphs can't be bipartite, so I was wondering whether it is possible for such a graph to have no even cycle. It turns out that graphs with no even cycle have at most (3n-3)/2 edges (I think), whereas my graphs have exactly (3n-2)/2 edges!

Is oeis for graph sequences feasible? Would canonical labellings and graph6 be enough or have I overlooked something (I don't understand these things). Toy use case: I come across the graphs obtained from even cycles by adding edges between opposite vertices. I write a program that generates the first ten graph6 reps and search them. The oegs entry tells me (amongst other things) hey those are also the mobius ladders!

Came across the fibonacci word the other day: s₀=0 s₁=01 sᵢ =sᵢ₋₁||sᵢ₋₂ (string concatenation). The limit is 0100101001001... seems to have only a passing resemblance to the fib numbers... but look at y=x/φ in R² and consider where it intersects the grid with vertices in N² - write a 0 when it intersects a vertical line and 1 when it intersects a horizontal line and you get 0100101001001... !!
https://en.wikipedia.org/wiki/Fibonacci_word

The possibility of future life making use of the rotational energy of black holes needs a catchy name. I suggest: rotosynthesis.

For some silly reason I have been in base 4 this afternoon. At first I was converting back and forth from base 10, but (surprisingly) quickly I got used to doing arithmetic directly without translation. Unfortunately I can't seem to do the same thing with currencies; I've been in the Czech republic for six months and I still think in Euros (apart from beer)

From the amazon review of one of the volumes of Gibbons "History of the Decline and Fall of the Roman Empire":

"The Romans developed an extreme toughness and vindictiveness on account of being made fun of by uncouth barbarians for the sissy "W" sound of the V in classical Latin. Every time a strapping, macho gaul heard the pathetic-sounding 'weeny weedy weesy' and broke into a raucous, howling laughter, every Roman in earshot burned with shame and dreams of revenge."