# [R] Permutations

Tue Jul 13 22:12:46 CEST 2004

```I may be confused, but I think what you described will produce greater than
472 million permutations.  I think your second permutation <1 2 4 | 3 5 6 |
7 8 9 | 10 11 12   YES-----2nd permutation> shows that you want more than
just a permutation of entire blocks.

There are a total of 12! (12 factorial) permutations of 1:12 ignoring your
blocking restriction.

There are 3! * 9! Permutations in which the first block has an intrablock
permutation and the rest of the 9 symbols can do anything.  Since there are
4 blocks then there are fewer than 4 * 3! * 9! permutations with intra-block
transfers (this 4*3!*9! double counts some intrablock permutations - you
need to take out of the 9! the count of intra-block only permutations among
the remaining 9 symbols: 3!*3!*3!).

This gives more than
12! - 4*3!*9! + 1 = 9!*[12*11*10 - 4*3*2*1] + 1 = 12*9![110 - 2] + 1 ~ 472
million permutations.

How could you possibly deal with all of these permutations?  If you can deal
with this much junk then maybe you can generate all 12! Permutations and
take out the ones you don't want.

Sorry if I got it totally wrong
bob

-----Original Message-----
From: Jordi Altirriba Gutiérrez [mailto:altirriba at hotmail.com]
Sent: Tuesday, July 13, 2004 3:07 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Permutations

Dear R users,
I'm a beginner user of R and I've a problem with permutations that I don't
know how to solve. I've 12 elements in blocks of 3 elements and I want only
to make permutations inter-blocks (no intra-blocks) (sorry if the
terminology is not accurate), something similar to:

1 2 3 | 4 5 6 | 7 8 9 | 10 11 12   ----------1st permutation

1 3 2 | 4 5 6 | 7 8 9 | 10 11 12   NO
-  -
3 2 1 | 4 5 6 | 7 8 9 | 10 11 12   NO
-  -  -
1 2 4 | 3 5 6 | 7 8 9 | 10 11 12   YES-----2nd permutation
-    -
4 5 6 | 1 2 3 | 7 8 9 | 10 11 12   YES-----3rd permutation
-  -  -   -  -  -
4 5 6 | 2 1 3 | 7 8 9 | 10 11 12   NO
-  -
....

Jordi Altirriba
Ph D student

Hospital Clinic - Barcelona - Spain

MSN Motor. http://motor.msn.es/researchcentre/

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