Partition of a set.

consider a partition of X= with where denotes the union of disjoint sets.

Remark that ,

I would like to implement the matlab code for above partition.

Please help me .

Thanks in advance.

[Rik]

Can you give an example of input and expected output in Matlab syntax?

[rohini more]

Let n=7, L=4

If I split n is following way

n=1+2+3+1 according to that [n]={1}

[rohini more]

Input is n=7 and L=4

Output should be

n=1+2+3+1, [n]=

where h1=1,h2=2 ,h3=3,h4=1 and H1={1},H2={2,3}, H3={4,5,6},H4={7}

Answer 1

[Bruno Luong]

https://www.mathworks.com/matlabcentral/fileexchange/17818-all-permutations-of-integers-with-sum-criteria

>> N=5; L=3;
>> h=allVL1(L,N-L)+1;
>> H=arrayfun(@(r) mat2cell(1:N,1,h(r,:)),(1:size(h,1))','unif',false);
>> DispPartObj(H) % FEX in my other answer
The 6 partition(s) are:
	{1} {2} {3 4 5}
	{1} {2 3} {4 5}
	{1} {2 3 4} {5}
	{1 2} {3} {4 5}
	{1 2} {3 4} {5}
	{1 2 3} {4} {5}

[rohini more]

Okay.

Thank you very much.

[rohini more]

Suppose I would like to consider random partition of set what changes I have to do in this code.

Thanks in advance.

Answer 2

[Bruno Luong]

https://www.mathworks.com/matlabcentral/fileexchange/24133-set-partition

>> N=5; L=3;
>> DispPartObj(SetPartition(N,L))
The 25 partition(s) are:
	{1 2 3} {4} {5}
	{1 2 4} {3} {5}
	{1 2} {3 4} {5}
	{1 3 4} {2} {5}
	{1 3} {2 4} {5}
	{1 4} {2 3} {5}
	{1} {2 3 4} {5}
	{1 2 5} {3} {4}
	{1 2} {3 5} {4}
	{1 2} {3} {4 5}
	{1 3 5} {2} {4}
	{1 3} {2 5} {4}
	{1 3} {2} {4 5}
	{1 5} {2 3} {4}
	{1} {2 3 5} {4}
	{1} {2 3} {4 5}
	{1 4 5} {2} {3}
	{1 4} {2 5} {3}
	{1 4} {2} {3 5}
	{1 5} {2 4} {3}
	{1} {2 4 5} {3}
	{1} {2 4} {3 5}
	{1 5} {2} {3 4}
	{1} {2 5} {3 4}
	{1} {2} {3 4 5}

[rohini more]

Okay.

Thank you.