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Forum index » Science and Technology » Math » Combinatorics
How many zigzag permutations?
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Proginoskes
science forum Guru


Joined: 29 Apr 2005
Posts: 2593

PostPosted: Tue Jul 04, 2006 10:33 pm    Post subject: Re: How many zigzag permutations? Reply with quote

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
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Feng
science forum beginner


Joined: 03 Feb 2006
Posts: 2

PostPosted: Tue Jul 04, 2006 7:07 pm    Post subject: How many zigzag permutations? Reply with 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.
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Google

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