Gavran's latest activity

I am not sure about this. In my opinion, we deal with combinations. Two long positive event cycles with the same elements must be equal...

I agree with all that you said in post #15, but is it okay to use the term “permutation” here? The expression $$ \binom{n-2}{l-1} $$...

I suppose that by "event" you mean a permutation that complies with the constraints imposed by the problem. The number of positive...

Then you end up with your own personal, probably inconsistent, mathematics.

Now we can use the above to calculate how many events with a positive outcome there are. For the general case when there are n...

People accept mathematical concepts much better if they can see their practical applications and relevance.

One should not forget that algebra does not pop out of a vacuum. It is preceded by arithmetic which develops the necessary reasoning...

Yes. In the notation I'm using, for ##~l>1~## the long cycle is of the form ##~(1,k_2,k_3,\dots,k_l)~## , meaning: passenger 1 sits in...

I suppose that by the l-th element in this scenario, you are referring to the 100th passenger who is taking seat #1. Any cycle that...

You are right. I didn't go into it, since the goal was to show the symmetry, and these details don't affect the result. In hindsight, I...

When I wrote "Considering small numbers is always a good strategy when you can't figure out the idea without it", I didn't mean it is a...

No. Its not you. I am not sure why the OP did not simply write: "consider the following sequence": 1 - 2 + 1 = 0 1 + 2 - 3 + 2 + 1 =...

Congrats , @TensorCalculus ! And, yes, you have made an impact ! In particular, your suggestion of having a way for members to...

That's not what I meant. There are lots of examples (e.g. Monty Hall), where the intuitive "it must be 1/2" argument is wrong. It's...