One idea I had: if you take a cycle and add a path between two of its vertices, you get a graph with three cycles. If you repeat, you either get six or seven depending on the choice of vertices. That means you can only achieve four or five cycles by gluing two graphs at a vertex, which I used to figure out a₄ and a₅.

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Here's a sequence that doesn't appear to be in the oeis (unless I erred). Let aₙ be the size of the smallest graph with exactly n cycles. The first few terms are: 3,5,4,6...
a₅ is pretty hard to figure out by hand (I think the answer is 8) but it's easy to check that a₆=5 a₇=4.
A trivial upper bound on aₙ is 2n+1. I think there should be a not too difficult upper bound of O(√n).
Anyone know anything else?

My office mate and I failed, in quick succession, to correctly divide 60 by 5. Time to go home I guess.

Nowadays every mathematics article goes online somewhere, and I would guess that the vast majority of article-reading is done on a screen of some kind. But the format stays the same, i.e. a long linear pdf of results, even if the dependencies between sections, lemmas, theorems etc are more like a tree. Has anyone done something like a mini wiki for an article, or in place of an article?

I wonder which has been written/typed more in human history: "(" or ")". Obviously parentheses are accidentally left open, but on the other hand it's quite common for Russians (and presumably others) to type "))))))))" as a form of emoticon. Do these balance out? Are there other times that one gets used without the other?

Or have I got it wrong and 2m is the distance in America too? I'm sure I heard 6ft a lot when I was there last month...

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In Europe the recommended distance is 2m, in America 6ft (which is approx 90% of 2m). Are humans good enough at distance estimation for this to make a difference? Probably there are too many other factors to figure this out from data.

Sorry if this turns out to be a silly question, but I couldn't find (or think of) an answer.

Suppose I add edges at random to a set of vertices until I have a connected graph. What is the expected number of cut vertices?

I'd be interested to know if there's a spike in sci-hub traffic what with universities being closed. It's often quicker to paste a doi into sci-hub than go through the remote access rigmarole. Or so I'm told...

Drawing a blank:

Is there a name for the "all-or-none" logical operator? Or more specifically its negation, which is XOR for 2-inputs but I want the general case.

Met a woman who seemed to think of herself as a non-math person (though she didn't say it out loud), whose son had asked her how many points were in a circle. I didn't want to give a boring closed answer, so, thinking of eg the ℓ₁ norm, I started to say "it depends..." and she finished the sentence saying "..on how many dimensions you have?" :D

Needless to say, I congratulated her on an excellent observation!

On my next birthday I'll be 25... sorry I mean 2^5

Came across quite a nice little graph that I feel should be "known" if anyone is interested:

I'm getting tired of living in cities that are growing. It means living in, and navigating around, building sites all the time. But what's the alternative? Places that are on the way down are pretty grim and difficult to live in as well. There can't be many cities whose population is stable. Maybe the thing to look at is the second derivative.

I don't see why insisting our colleagues have inclusive values is just as bad as insisting our colleagues have exclusive values. In fact I don't see why insisting on some values is bad per se, it clearly depends on the values in question.

The argument that diversity statements harm the very people they are intended to help is much more convincing to me.

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

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