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Feng
science forum beginner

Joined: 03 Feb 2006
Posts: 2

Posted: Tue Jul 04, 2006 7:07 pm    Post subject: How many zigzag permutations?

Given n, how many of the n! permutations are zigzags? For example, the
zigzags for small n's are:
{1} for n=1;
{12, 21} for n=2;
{132, 213, 231, 312} for n=3;

Is there a general formula for arbitrary n? The first thing I noticed
is that the number of zigzags has to be even for n>1, because the
reverse of a zigzag is again a zigzag.
Proginoskes
science forum Guru

Joined: 29 Apr 2005
Posts: 2593

Posted: Tue Jul 04, 2006 10:33 pm    Post subject: Re: How many zigzag permutations?

Feng wrote:
 Quote: Given n, how many of the n! permutations are zigzags? For example, the zigzags for small n's are: {1} for n=1; {12, 21} for n=2; {132, 213, 231, 312} for n=3; Is there a general formula for arbitrary n? The first thing I noticed is that the number of zigzags has to be even for n>1, because the reverse of a zigzag is again a zigzag.

Google is your friend. (Or any other search engine.)

MathWorld is your friend.

A search for "zigzag permutations" led to the MathWorld page, which
calls them "alternating permutations", and the page at

http://mathworld.wolfram.com/AlternatingPermutation.html

has a lot of information, including how to calculate the number of
zigzags.

--- Christopher Heckman
Google

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