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Feng
science forum beginner
Joined: 03 Feb 2006
Posts: 2
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 Posted: Tue Jul 04, 2006 7:07 pm Post subject:
How many zigzag permutations?
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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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Proginoskes
science forum Guru
Joined: 29 Apr 2005
Posts: 2593
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| Posted: Tue Jul 04, 2006 10:33 pm Post subject:
Re: How many zigzag permutations?
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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.
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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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