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

[Ron Hardin]

Trying proof again (the first k-1 evens don't have to go to the first k-1 odds 
but can go to any odd)

4 choosings:

Order the even elements (factorial((n+1)/2))
Order the  odd elements (factorial(n/2))
The first k-1 even elements go somewhere in the odd elements (binomial(n/2,k-1))
The first k-1 odd elements go somewhere in the even elements 
(binomial((n+1)/2,k-1))
The even and odd elements after k-1 fill the empty even and odd slots 
respectively in the chosen order

Waiting five minutes this time.  Still seems okay.

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 7:16:30 AM
> Subject: [seqfan] Re: Permutations with 2K-2 odd displacements, formula?
> 
> Sorry, the proof is nonsense.  Something like the proof is right.