# [seqfan] Re: Permutations with 2K-2 odd displacements, formula?

Ron Hardin rhhardin at att.net
Sun Jun 2 13:16:20 CEST 2013

```Sorry, the proof is nonsense.  Something like the proof is right.

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Sun, June 2, 2013 7:05:24 AM
> Subject: [seqfan] Re: Permutations with 2K-2 odd displacements, formula?
>
> I suppose it's easy to prove, given the answer
>
> Define a permutation by  four choosings:
>
> Order the even elements (factorial((n+1)/2))
> Order the  odd elements (factorial(n/2))
> The first k-1 even elements go to the first k-1  odd elements in all ways
> (binomial(n/2,k-1))
> The first k-1 odd elements  go to the first k-1 even elements in all ways
> (binomial((n+1)/2,k-1))
>
> The remaining even elements appear in  unfilled even slots in their new order
> The remaining odd elements appear in  unfilled odd slots in their new order
>
> Assuming this is right, the word  empirical can be dropped and the formula gets
>
> promoted to the title, and the  problem to a comment.
```