[R] Generating groupings of ordered observations

[Gavin Simpson]

Dear List,

I have a problem I'm finding it difficult to make headway with.

Say I have 6 ordered observations, and I want to find all combinations
of splitting these 6 ordered observations in g groups, where g = 1, ...,
6. Groups can only be formed by adjacent observations, so observations 1
and 4 can't be in a group on their own, only if 1,2,3&4 are all in the
group.

For example, with 6 observations, the columns of the matrices below
represent the groups that can be formed by placing the 6 ordered
observations into 2-5 groups. Think of the columns of these matrices as
being an indicator of group membership. We then cbind these matrices
with the trivial partitions into 1 and 6 groups:

mat2g <- matrix(c(1,1,1,1,1,
                  2,1,1,1,1,
                  2,2,1,1,1,
                  2,2,2,1,1,
                  2,2,2,2,1,
                  2,2,2,2,2),
                nrow = 6, ncol = 5, byrow = TRUE)

mat3g <- matrix(c(1,1,1,1,1,1,1,1,1,1,
                  2,2,2,2,1,1,1,1,1,1,
                  3,2,2,2,2,2,2,1,1,1,
                  3,3,2,2,3,2,2,2,2,1,
                  3,3,3,2,3,3,2,3,2,2,
                  3,3,3,3,3,3,3,3,3,3),
                nrow = 6, ncol = 10, byrow = TRUE)

mat4g <- matrix(c(1,1,1,1,1,1,1,1,1,1,
                  2,2,2,2,2,2,1,1,1,1,
                  3,3,3,2,2,2,2,2,2,1,
                  4,3,3,3,3,2,3,3,2,2,
                  4,4,3,4,3,3,4,3,3,3,
                  4,4,4,4,4,4,4,4,4,4),
                nrow = 6, ncol = 10, byrow = TRUE)

mat5g <- matrix(c(1,1,1,1,1,
                  2,2,2,2,1,
                  3,3,3,2,2,
                  4,4,3,3,3,
                  5,4,4,4,4,
                  5,5,5,5,5),
                nrow = 6, ncol = 5, byrow = TRUE)

cbind(rep(1,6), mat2g, mat3g, mat4g, mat5g, 1:6)

I'd like to be able to do this automagically, for any (reasonable,
small, say n = 10-20) number of observations, n, and for g = 1, ..., n
groups.

I can't see the pattern here or a way forward. Can anyone suggest an
approach?

Thanks in advance,

Gavin

-- 
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 Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
 ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
 Pearson Building,             [e] gavin.simpsonATNOSPAMucl.ac.uk
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