Finding A List of All Combinations of 6 Numbers That Add up to 10

So I've seen similar versions of this question asked before (Getting all combinations which sum up to 100 using R) but I'm struggling to find a way to figure out what I need to run specifically. I'm trying to create a list in R of all the different combinations of 6 numbers that add up to 10. However, I want to include 0s and repeats of the same # in the row. So it would look something like this:

10 0 0 0 0 0 9 1 0 0 0 0 8 2 0 0 0 0 I've tried running the following:

C = t(restrictedparts(10,6, include.zero=TRUE))
ComboSet<-data.frame(do.call(rbind, lapply(1:nrow(C),function(i) getall(iterpc(table(C[i,]), order=T)))))

However, when I do this it does not seem to include the variations that have 0s in them. I've tried entering the include.zero=TRUE function into different parts of what I'm running but I've had no luck so far. Any suggestions?

This is a good question and the answer isn't very obvious.

There are many things to address here. For starters, make sure that you include the libraries that you use in your example. I know from experience that you are using partitions and iterpc. From the partitions documentation, we see that there is a function that returns exactly what you are looking for without any additional steps. It is the compositions function which generates Integer Compositions.

myComps <- t(as.matrix(compositions(10, 6)))
head(myComps)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]   10    0    0    0    0    0
[2,]    9    1    0    0    0    0
[3,]    8    2    0    0    0    0
[4,]    7    3    0    0    0    0
[5,]    6    4    0    0    0    0
[6,]    5    5    0    0    0    0

dim(myComps)
[1] 3003    6

all(rowSums(myComps) == 10)
[1] TRUE

As for fixing your actual code, I'm not exactly sure why your code is not working as is. I've used iterpc in the past and remember explicitly using that same approach. Anywho, the workaround is to explicitly declare the labels parameter as the frequency of each element is being used instead of the value itself.

## The 1's should be 0's and the 2's should be 10's
ComboSet[1:6, ]
X1 X2 X3 X4 X5 X6
1  1  1  1  1  1  2
2  1  1  1  1  2  1
3  1  1  1  2  1  1
4  1  1  2  1  1  1
5  1  2  1  1  1  1
6  2  1  1  1  1  1

## OP's original code
ComboSet<-data.frame(do.call(rbind, lapply(1:nrow(C),function(i) getall(iterpc(table(C[i,]), order=T)))))

all(rowSums(ComboSet) == 10)
[1] FALSE

table(rowSums(ComboSet))

7   8   9  10  11  12  13  14  15  16 
12  30 150 255 186 690 420 420 180 660

## Here is the fix with labels explicitly declared
ComboSetFix <- data.frame(do.call(rbind, lapply(1:nrow(C), function(i) {
    getall(iterpc(table(C[i,]), labels = as.integer(names(table(C[i,]))), order=T))
})))

all(rowSums(ComboSetFix) == 10)
[1] TRUE

dim(ComboSetFix)
[1] 3003    6

You should know that iterpc is not being actively maintained and users are encouraged to switch to arrangements. It has a different interface, so you can't simply replace the word "iterpc" with "arrangements".

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