# Re: [R] Permutations

From: Jordi Altirriba Gutiérrez <altirriba_at_hotmail.com>
Date: Thu 15 Jul 2004 - 03:42:49 EST

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 YES-------1st permutation

1 3 2 | 4 5 6 | 7 8 9 | 10 11 12 NO ----because it's an "intra-block" permutation of permutation 1

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 ----because it's an "intra-block" permutation of permutation 3

• - 10 1 7 | 4 8 7 | 5 6 12 | 3 2 9 YES---Xth permutation

1 10 7 | 4 8 7 | 5 6 12 | 3 2 9 NO ----because it's an "intra-block"permutation of permutation X - -

So, what is a "not correct" permutation is an "intra-block" permutation of a permutation created before.

Again, thanks for your time and suggestions,

Jordi Altirriba
PhD student
Hospital Clinic - Barcelona - Spain

P.S. Probably (it's the way of how I'm testing the algorithms now with Excel) [sorry if it's stupid], could be interesting something similar to:

1 2 3 | 4 5 6 | 7 8 9 | 10 11 12 ---> 1*2*3=6 | 4*5*6=120 | 7*8*9=504 | 10*11*12=1320

1 3 2 | 4 5 6 | 7 8 9 | 10 11 12 ---> 1*3*2=6 | 4*5*6=120 | 7*8*9=504 | 10*11*12=1320

4 5 6 | 1 2 3 | 7 8 9 | 10 11 12 ---> 4*5*6=120 | 1*2*3=6 | 7*8*9=504 | 10*11*12=1320

Results:

```permutation1: 6 | 120 | 504 | 1320
permutation2: 6 | 120 | 504 | 1320
permutation3: 120 | 6 | 504 | 1320

```

Order the permutations according first to the first parameter, second to the second...and to the fourth.

In this case it's the same:

```permutation1: 6 | 120 | 504 | 1320
permutation2: 6 | 120 | 504 | 1320
permutation3: 120 | 6 | 504 | 1320

```

Therefore, if the first, second, third and fourth parameter of a permutations have the same value that the next permutation it's because there is an "intra-block" permutation. So, permutation 2 is an "intra-block" permutation of permutation 1.

P.S. Sorry for having forgotten the title of the last e-mail

>To: Jordi Altirriba Gutiérrez <altirriba@hotmail.com>
>CC: rksh@soc.soton.ac.uk, R-help <r-help@stat.math.ethz.ch>
>Subject: Re: [R] Permutations
>Date: Wed, 14 Jul 2004 18:00:49 +0100
>
>I think the issue here is in the two keywords - permutations or sample.
>
>AFAIK, permutations should return all admissible (by some rule)
>combinations. If this is a large number, as some have pointed out, then
>one essentially takes a _sample_ of all admissible combinations. Since
>you earlier mentioned that you only want 5-10 outputs, perhaps the
>correct term is sampling with restrictions.
>
>There main problem with Robin's method in that all elements within a row
>are mutually exclusive to the other. e.g. only one of either 1, 4, 7, 10
>can appear in block 1. Furthermore they can only appear in the first
>slot of the first block (so no intra-block randomness). This limits the
>number of possible outputs.
>
>Can you clearly define the rules (with examples) for an admissible
>combination ? They seem to have a different meaning every time I read
>the mail. Maybe I am just confused.
>
>
>On Wed, 2004-07-14 at 17:16, Jordi Altirriba GutiÃ©rrez wrote:
> > Dear R users,
> > First of all, thanks to Rolf, Brad, Robin, Erich, Fernando and
> > for your time and suggestions.
> > Ive been testing some algorithms (sorry for the delay, Im very slow,
>and
> > Im a completely beginner in Rs world).
> > First, the Robin algorithm.
> > I think that there is a problem because Ive done 200 permutations and
> > Ive found that these permutations are the same:
> > 52 and 91, 99 and 110, 121 and 122, 51 and 141, 130 and 134.
> > Thanks again,
> >
> > Jordi Altirriba
> > Hospital Clinic Barcelona - Spain
> >
> > >x <- c(1,2,3,4,5,6,7,8,9,10,11,12)
> > >dim(x) <- c(3,4) a<-matrix(1,200,12)
> > >for (i in 1:200)
> > + {
> > + jj <- t(apply(x,1,sample))
> > + a[i,]<-as.vector(jj)
> > + }
> > >a
> > [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
> > [1,] 7 2 3 1 11 6 4 8 9 10 5 12
> > [2,] 1 2 9 7 11 6 4 8 12 10 5 3
> > [3,] 7 2 9 1 11 3 4 5 6 10 8 12
> > [4,] 10 8 6 4 5 12 7 2 9 1 11 3
> > [5,] 10 2 12 1 11 9 7 8 6 4 5 3
> > [6,] 7 8 6 1 5 9 4 11 12 10 2 3
> > [7,] 1 5 12 7 2 6 4 8 9 10 11 3
> > [8,] 1 5 9 10 8 6 4 2 3 7 11 12
> > [9,] 1 11 6 7 2 12 4 5 9 10 8 3
> > [10,] 4 5 12 10 11 9 1 8 6 7 2 3
> > [11,] 1 11 9 7 5 6 4 8 12 10 2 3
> > [12,] 1 8 3 4 2 12 10 5 9 7 11 6
> > [13,] 1 2 3 7 11 6 10 5 12 4 8 9
> > [14,] 4 8 3 10 5 12 7 2 9 1 11 6
> > [15,] 10 2 3 4 8 6 7 11 9 1 5 12
> > [16,] 4 8 9 10 2 12 7 5 6 1 11 3
> > [17,] 1 2 6 10 5 3 7 8 12 4 11 9
> > [18,] 10 2 9 4 11 12 1 5 6 7 8 3
> > [19,] 4 8 6 7 11 12 1 2 9 10 5 3
> > [20,] 1 8 12 7 2 3 10 11 6 4 5 9
> > [21,] 10 2 12 1 5 9 7 11 6 4 8 3
> > [22,] 4 11 12 1 2 3 10 8 6 7 5 9
> > [23,] 1 11 3 7 2 6 10 5 9 4 8 12
> > [24,] 7 2 9 10 5 12 1 11 3 4 8 6
> > [25,] 7 8 9 1 2 6 4 5 3 10 11 12
> > [26,] 4 5 12 10 2 3 7 11 6 1 8 9
> > [27,] 4 5 9 1 11 3 7 8 12 10 2 6
> > [28,] 1 5 6 4 11 3 7 8 9 10 2 12
> > [29,] 4 5 6 1 11 9 10 2 12 7 8 3
> > [30,] 4 11 3 7 8 12 10 5 6 1 2 9
> > [31,] 10 2 3 1 11 6 7 8 9 4 5 12
> > [32,] 10 2 3 7 8 9 1 11 6 4 5 12
> > [33,] 7 11 6 1 8 9 4 5 12 10 2 3
> > [34,] 7 5 12 1 8 6 4 11 3 10 2 9
> > [35,] 1 2 3 4 8 6 7 5 9 10 11 12
> > [36,] 7 8 3 1 11 9 10 2 12 4 5 6
> > [37,] 10 2 6 1 11 12 7 5 3 4 8 9
> > [38,] 1 5 9 4 11 12 7 8 3 10 2 6
> > [39,] 1 2 12 7 5 9 10 8 3 4 11 6
> > [40,] 1 8 3 10 2 12 7 11 6 4 5 9
> > [41,] 1 2 9 4 8 3 10 11 12 7 5 6
> > [42,] 4 5 6 1 2 9 10 8 3 7 11 12
> > [43,] 1 2 6 7 11 12 10 5 9 4 8 3
> > [44,] 1 2 9 10 11 12 4 8 6 7 5 3
> > [45,] 10 5 9 7 11 6 4 2 3 1 8 12
> > [46,] 1 2 3 4 11 6 7 5 9 10 8 12
> > [47,] 4 2 6 1 8 3 10 5 12 7 11 9
> > [48,] 4 8 9 7 2 3 1 5 12 10 11 6
> > [49,] 10 8 12 1 2 9 4 11 3 7 5 6
> > [50,] 10 8 6 1 2 3 7 5 12 4 11 9
> > [51,] 7 2 12 10 11 6 4 8 3 1 5 9
> > [52,] 4 5 6 1 2 12 10 11 9 7 8 3
> > [53,] 1 2 3 7 5 6 4 8 9 10 11 12
> > [54,] 10 5 3 7 11 9 1 8 6 4 2 12
> > [55,] 7 11 12 4 2 3 10 8 6 1 5 9
> > [56,] 1 5 9 4 11 12 10 8 3 7 2 6
> > [57,] 4 5 9 7 11 3 10 2 6 1 8 12
> > [58,] 10 11 3 4 5 6 1 8 12 7 2 9
> > [59,] 4 8 9 10 5 6 7 2 3 1 11 12
> > [60,] 4 2 12 1 8 6 10 5 9 7 11 3
> > [61,] 4 8 6 7 11 9 10 5 12 1 2 3
> > [62,] 7 8 3 10 5 6 1 11 12 4 2 9
> > [63,] 10 5 3 7 8 6 1 2 9 4 11 12
> > [64,] 10 2 9 4 11 12 1 5 3 7 8 6
> > [65,] 1 11 6 4 8 12 7 2 3 10 5 9
> > [66,] 1 5 3 7 11 9 4 2 12 10 8 6
> > [67,] 4 2 6 7 5 12 10 8 9 1 11 3
> > [68,] 4 11 12 10 2 3 7 8 6 1 5 9
> > [69,] 4 5 6 10 2 3 7 8 9 1 11 12
> > [70,] 1 11 12 10 2 6 4 5 3 7 8 9
> > [71,] 10 5 6 7 8 12 4 2 9 1 11 3
> > [72,] 10 8 12 1 11 9 7 5 3 4 2 6
> > [73,] 10 8 3 7 11 9 4 5 12 1 2 6
> > [74,] 7 2 12 1 5 6 4 8 9 10 11 3
> > [75,] 7 2 12 10 8 9 1 11 6 4 5 3
> > [76,] 7 2 3 1 5 9 4 8 12 10 11 6
> > [77,] 1 11 3 10 5 6 7 2 9 4 8 12
> > [78,] 7 2 6 10 11 12 4 8 9 1 5 3
> > [79,] 10 8 6 7 5 3 1 2 9 4 11 12
> > [80,] 10 11 3 7 2 12 4 8 6 1 5 9
> > [81,] 10 5 6 1 8 3 4 11 9 7 2 12
> > [82,] 1 11 3 7 5 12 10 2 6 4 8 9
> > [83,] 4 11 9 10 5 12 7 2 6 1 8 3
> > [84,] 1 11 12 7 8 3 4 2 6 10 5 9
> > [85,] 10 2 9 7 5 6 1 11 12 4 8 3
> > [86,] 7 11 9 4 5 6 10 2 12 1 8 3
> > [87,] 4 5 12 7 2 3 10 11 6 1 8 9
> > [88,] 1 2 12 7 5 3 10 8 6 4 11 9
> > [89,] 1 8 12 7 11 9 10 2 6 4 5 3
> > [90,] 4 5 3 10 11 9 7 2 6 1 8 12
> > [91,] 4 5 6 1 2 12 10 11 9 7 8 3
> > [92,] 10 11 9 7 5 12 1 2 6 4 8 3
> > [93,] 4 2 3 7 8 6 1 11 12 10 5 9
> > [94,] 4 5 3 10 2 12 7 8 9 1 11 6
> > [95,] 4 8 3 10 11 9 1 2 6 7 5 12
> > [96,] 7 5 12 10 11 3 1 8 9 4 2 6
> > [97,] 4 2 3 1 8 6 7 11 9 10 5 12
> > [98,] 4 11 9 7 5 12 10 8 6 1 2 3
> > [99,] 1 11 12 4 5 6 7 8 3 10 2 9
> > [100,] 1 8 3 7 5 6 10 2 12 4 11 9
> > [101,] 7 11 6 4 8 3 1 2 12 10 5 9
> > [102,] 7 11 12 1 2 3 10 8 6 4 5 9
> > [103,] 4 5 12 1 2 9 7 8 3 10 11 6
> > [104,] 10 11 12 4 8 3 7 5 9 1 2 6
> > [105,] 10 5 9 1 2 3 4 8 6 7 11 12
> > [106,] 10 11 9 1 2 12 7 8 3 4 5 6
> > [107,] 10 11 3 4 8 9 7 5 12 1 2 6
> > [108,] 7 2 6 1 11 9 4 5 12 10 8 3
> > [109,] 1 8 6 7 2 12 10 5 3 4 11 9
> > [110,] 1 11 12 4 5 6 7 8 3 10 2 9
> > [111,] 7 8 6 1 5 3 10 2 12 4 11 9
> > [112,] 4 8 3 7 5 6 1 2 9 10 11 12
> > [113,] 1 2 9 4 11 6 7 5 3 10 8 12
> > [114,] 4 11 9 1 8 6 7 2 3 10 5 12
> > [115,] 10 8 3 4 11 12 7 2 9 1 5 6
> > [116,] 7 11 12 1 2 3 4 8 9 10 5 6
> > [117,] 1 5 3 10 11 12 7 8 9 4 2 6
> > [118,] 1 11 6 4 2 9 10 5 12 7 8 3
> > [119,] 10 2 3 1 5 9 4 8 12 7 11 6
> > [120,] 1 2 3 4 11 12 7 8 9 10 5 6
> > [121,] 7 8 3 4 5 12 10 2 6 1 11 9
> > [122,] 7 8 3 4 5 12 10 2 6 1 11 9
> > [123,] 4 5 3 10 11 9 7 8 6 1 2 12
> > [124,] 4 5 6 7 11 9 1 8 12 10 2 3
> > [125,] 10 8 6 1 11 9 4 2 12 7 5 3
> > [126,] 10 8 12 4 11 9 7 2 6 1 5 3
> > [127,] 7 8 12 1 11 6 10 5 9 4 2 3
> > [128,] 1 8 12 10 11 3 7 5 9 4 2 6
> > [129,] 7 8 3 10 2 6 1 11 9 4 5 12
> > [130,] 7 11 9 1 2 6 10 8 3 4 5 12
> > [131,] 10 2 3 4 11 9 1 5 6 7 8 12
> > [132,] 4 11 3 1 5 9 10 2 6 7 8 12
> > [133,] 10 2 12 7 8 3 4 5 6 1 11 9
> > [134,] 7 11 9 1 2 6 10 8 3 4 5 12
> > [135,] 7 8 3 4 11 6 10 2 9 1 5 12
> > [136,] 10 8 9 7 11 12 1 2 6 4 5 3
> > [137,] 10 8 12 4 5 3 1 2 9 7 11 6
> > [138,] 1 2 6 10 8 12 7 11 9 4 5 3
> > [139,] 4 5 3 7 11 9 1 2 12 10 8 6
> > [140,] 4 5 12 7 8 6 10 11 3 1 2 9
> > [141,] 7 2 12 10 11 6 4 8 3 1 5 9
> > [142,] 10 11 12 7 2 6 1 5 3 4 8 9
> > [143,] 7 2 3 10 11 6 1 8 9 4 5 12
> > [144,] 1 2 9 10 5 12 4 8 3 7 11 6
> > [145,] 1 11 6 4 8 9 7 5 12 10 2 3
> > [146,] 4 5 3 10 2 6 1 11 9 7 8 12
> > [147,] 7 11 9 1 2 3 10 8 12 4 5 6
> > [148,] 4 2 3 1 5 12 7 8 6 10 11 9
> > [149,] 10 11 12 4 8 3 1 2 9 7 5 6
> > [150,] 4 8 3 10 5 6 1 11 9 7 2 12
> > [151,] 1 8 6 10 5 9 4 11 3 7 2 12
> > [152,] 4 8 6 7 11 12 10 5 3 1 2 9
> > [153,] 7 2 3 10 5 6 4 11 9 1 8 12
> > [154,] 10 5 12 1 8 9 7 2 3 4 11 6
> > [155,] 1 8 6 4 2 9 10 5 3 7 11 12
> > [156,] 10 2 3 7 5 9 4 11 12 1 8 6
> > [157,] 10 5 3 1 2 6 7 8 9 4 11 12
> > [158,] 7 11 12 4 5 9 10 8 3 1 2 6
> > [159,] 7 5 3 1 8 12 10 2 6 4 11 9
> > [160,] 7 2 6 4 11 3 1 5 12 10 8 9
> > [161,] 7 5 3 1 2 12 4 8 9 10 11 6
> > [162,] 7 8 12 1 5 6 10 11 9 4 2 3
> > [163,] 10 11 9 4 8 6 1 2 3 7 5 12
> > [164,] 7 11 6 1 5 9 4 2 12 10 8 3
> > [165,] 4 11 9 10 8 3 7 2 12 1 5 6
> > [166,] 4 2 6 10 8 9 7 11 12 1 5 3
> > [167,] 7 5 3 10 2 12 4 8 6 1 11 9
> > [168,] 1 8 12 7 2 3 4 5 9 10 11 6
> > [169,] 7 8 12 1 5 6 4 2 3 10 11 9
> > [170,] 4 5 3 7 8 9 1 2 12 10 11 6
> > [171,] 7 11 9 1 8 6 4 2 12 10 5 3
> > [172,] 10 8 3 1 2 9 4 11 12 7 5 6
> > [173,] 10 5 12 7 8 9 4 11 3 1 2 6
> > [174,] 10 11 6 7 5 3 4 8 12 1 2 9
> > [175,] 7 11 12 1 2 3 10 8 9 4 5 6
> > [176,] 1 11 12 7 2 3 4 8 9 10 5 6
> > [177,] 10 11 12 4 5 3 7 8 6 1 2 9
> > [178,] 10 5 3 7 2 6 4 8 12 1 11 9
> > [179,] 1 5 6 7 2 9 10 11 3 4 8 12
> > [180,] 1 11 12 10 5 6 4 2 3 7 8 9
> > [181,] 7 2 12 4 11 9 1 5 6 10 8 3
> > [182,] 10 11 12 1 5 3 7 8 9 4 2 6
> > [183,] 4 8 3 1 11 9 7 2 6 10 5 12
> > [184,] 4 8 9 7 2 3 10 5 6 1 11 12
> > [185,] 10 11 9 1 5 6 7 2 12 4 8 3
> > [186,] 10 5 12 4 8 9 7 2 6 1 11 3
> > [187,] 4 2 3 1 8 6 7 5 12 10 11 9
> > [188,] 10 2 9 4 11 12 1 8 3 7 5 6
> > [189,] 10 2 12 7 11 3 4 5 9 1 8 6
> > [190,] 4 5 6 7 8 3 10 11 9 1 2 12
> > [191,] 10 5 9 1 2 3 7 11 12 4 8 6
> > [192,] 4 11 9 7 2 6 10 5 3 1 8 12
> > [193,] 10 11 12 1 2 6 4 5 9 7 8 3
> > [194,] 10 2 3 4 11 12 7 5 6 1 8 9
> > [195,] 4 2 6 7 8 9 1 11 3 10 5 12
> > [196,] 10 2 12 4 8 6 7 5 3 1 11 9
> > [197,] 7 5 12 4 11 9 1 2 3 10 8 6
> > [198,] 10 5 6 1 11 3 7 2 9 4 8 12
> > [199,] 1 2 9 7 11 3 4 8 6 10 5 12
> > [200,] 4 8 3 7 11 12 1 2 6 10 5 9
> >
> >
> >
> > >From: Robin Hankin <rksh@soc.soton.ac.uk>
> > >To: Jordi Altirriba GutiÃ©rrez <altirriba@hotmail.com>
> > >CC: r-help@stat.math.ethz.ch
> > >Subject: Re: [R] (no subject) (was: Permutations)
> > >Date: Wed, 14 Jul 2004 09:11:48 +0100
> > >
> > >Jordi
> > >
> > >try this
> > >
> > >
> > >R> x <- c(1,2,3, 10,11,12, 41,42,43, 81,82,83)
> > >R> dim(x) <- c(3,4)
> > >R> x
> > > [,1] [,2] [,3] [,4]
> > >[1,] 1 10 41 81
> > >[2,] 2 11 42 82
> > >[3,] 3 12 43 83
> > >R> jj <- t(apply(x,1,sample))
> > >R> jj
> > > [,1] [,2] [,3] [,4]
> > >[1,] 1 41 10 81
> > >[2,] 2 11 82 42
> > >[3,] 12 3 43 83
> > >R> as.vector(jj)
> > >R>
> > > [1] 1 2 12 41 11 3 10 82 43 81 42 83
> > >
> > >
> > >
> > >
> > >and I think that does what you want...
> > >
> > >We take the vector, rearrange it into a matrix with three rows, then
>sample
> > >*within* the rows,
> > >then rearrange into a vector again.
> > >
> > >There will be one forbidden permutation, namely the identity (which may
>or
> > >may not be
> > >desirable).
> > >
> > >This method doesn't allow "intra block" permutations.
> > >
> > >best
> > >
> > >rksh
> > >
> > >
> > >
> > >> Dear R users,
> > >> First of all, thanks for the incredibly fast answers and help of
>Rolf,
> > >>Marc and Robert.
> > >> Yes, I noticed that it was a lot of permutacions, but my intention
>was
> > >>to make this process automatic and take only 5.000 - 10.000
>permutations.
> > >>Therefore, I wanted only to take that "interesting permutations" with
> > >>"some information" [inter-block permutations].
> > >> The reason why I'm interested in these permutations is because I'm
>using
> > >>some packages of Bioconductor to analyse my data from some microarrays
>and
> > >>I thought that perhaps could be interesting to see what happens when I
> > >>permute my data and I compare it against the not permuted data.
> > >> Thanks again for your time and suggestions.
> > >>
> > >>Jordi Altirriba
> > >>Ph. D. Student
> > >>
> > >>Hospital Clinic-Barcelona-Spain
> > >>
> > >>______________________________________________
> > >>R-help@stat.math.ethz.ch mailing list
> > >>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> > >>http://www.R-project.org/posting-guide.html
> > >
> > >
> > >--
> > >Robin Hankin
> > >Uncertainty Analyst
> > >Southampton Oceanography Centre
> > >SO14 3ZH
> > >tel +44(0)23-8059-7743
> > >initialDOTsurname@soc.soton.ac.uk (edit in obvious way; spam
>precaution)
> >
> > ______________________________________________
> > R-help@stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help