How can I create a set from elements and combined elements?

I have the following vector:

A = [1 2 3 4];

And all it's possible combinations, which I obtained by using the following code

n            = length(A);
combinations = {};
counter      = 1;
for i = 1:n
    CCC = nchoosek(gen,i);
    for j = 1 : size(CCC,1)
        combinations{counter,1} = CCC(j,:);
        counter = counter + 1;
    end
end

Then, I obtained the following result:

Now, I need to create something like this:

Note that elements don't repeat

Answer 1

[Bruno Luong]

Not sure exactly what kind of "combination" you look for, but it looks like a subset of these

b=logical(dec2bin(1:2^4-1,4)-'0');
% https://www.mathworks.com/matlabcentral/fileexchange/24133-set-partition
c=arrayfun(@(r) SetPartition(num2cell(find(b(r,:)))),1:size(b,1),'unif',0);
c=cat(1,c{:});
DispPartObj(c)

Gives this (notice 51 combinations here)

The 51 partition(s) are:
	{4}
	{3}
	{3 4}
	{3} {4}
	{2}
	{2 4}
	{2} {4}
	{2 3}
	{2} {3}
	{2 3 4}
	{2 3} {4}
	{2 4} {3}
	{2} {3 4}
	{2} {3} {4}
	{1}
	{1 4}
	{1} {4}
	{1 3}
	{1} {3}
	{1 3 4}
	{1 3} {4}
	{1 4} {3}
	{1} {3 4}
	{1} {3} {4}
	{1 2}
	{1} {2}
	{1 2 4}
	{1 2} {4}
	{1 4} {2}
	{1} {2 4}
	{1} {2} {4}
	{1 2 3}
	{1 2} {3}
	{1 3} {2}
	{1} {2 3}
	{1} {2} {3}
	{1 2 3 4}
	{1 2 3} {4}
	{1 2 4} {3}
	{1 2} {3 4}
	{1 2} {3} {4}
	{1 3 4} {2}
	{1 3} {2 4}
	{1 3} {2} {4}
	{1 4} {2 3}
	{1} {2 3 4}
	{1} {2 3} {4}
	{1 4} {2} {3}
	{1} {2 4} {3}
	{1} {2} {3 4}
	{1} {2} {3} {4}

[Bruno Luong]

EDIT bug on the answer

[Franklin Fabián Lucero Luna]

Thanks! It is useful!

When I use the code provded, I obtain the following result:

When I see c variable, I can find all the partitions I need, nevertheless, they are in a sublevel of the {} structure. How did you printed the partitions?

[Bruno Luong]

Can you try this?

b=logical(dec2bin(1:2^4-1,4)-'0');
% https://www.mathworks.com/matlabcentral/fileexchange/24133-set-partition
c=arrayfun(@(r) SetPartition(num2cell(find(b(r,:)))),1:size(b,1),'unif',0);
c=cat(1,c{:});
c=cellfun(@(c) cellfun(@(c) [c{:}], c, 'unif', 0), c, 'unif', 0);
DispPartObj(c)

Or use the bug-fix version of DispPartObj attached here

Answer 2

[KSSV]

You can initialize a cell and get what you want.

combination = cell(10,1) ; 
for i = 1:10
    combination{i} = ['combination',num2str(i)] ;    
end
combination

Like wise crate other cell with the name ExpectedResult and save the required data.

At the end, the generated cells can be converted to table as well.