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.

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?

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...

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!

https://www.ams.org/journals/notices/202001/rnoti-o1.pdf

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

Mathematician, computer scientist, bassist, knitter?

Joined Jan 2018