MATLAB: How to create permutations of multisets

Question

I have a vector with N=6 elements and q=3 elements symboled as 0, 1, 2.

I want to create all vectors consisted of N=6 elements such that:

• 2 elements out of N=6 are equal to 0,
• 2 elements out of N=6 are equal to 1,
• 2 elements out of N=6 are equal to 2

in all possible positions.

How can I create them?

The number of these vectors are equal to 90, that is:

[1,] 0 0 1 1 2 2

[2,] 0 0 1 2 1 2

[3,] 0 0 1 2 2 1

[4,] 0 0 2 1 1 2

[5,] 0 0 2 1 2 1

[6,] 0 0 2 2 1 1

[7,] 0 1 0 1 2 2

[8,] 0 1 0 2 1 2

[9,] 0 1 0 2 2 1

[10,] 0 1 1 0 2 2

[11,] 0 1 1 2 0 2

[12,] 0 1 1 2 2 0

[13,] 0 1 2 0 1 2

[14,] 0 1 2 0 2 1

[15,] 0 1 2 1 0 2

[16,] 0 1 2 1 2 0

[17,] 0 1 2 2 0 1

[18,] 0 1 2 2 1 0

[19,] 0 2 0 1 1 2

[20,] 0 2 0 1 2 1

[21,] 0 2 0 2 1 1

[22,] 0 2 1 0 1 2

[23,] 0 2 1 0 2 1

[24,] 0 2 1 1 0 2

[25,] 0 2 1 1 2 0

[26,] 0 2 1 2 0 1

[27,] 0 2 1 2 1 0

[28,] 0 2 2 0 1 1

[29,] 0 2 2 1 0 1

[30,] 0 2 2 1 1 0

[31,] 1 0 0 1 2 2

[32,] 1 0 0 2 1 2

[33,] 1 0 0 2 2 1

[34,] 1 0 1 0 2 2

[35,] 1 0 1 2 0 2

[36,] 1 0 1 2 2 0

[37,] 1 0 2 0 1 2

[38,] 1 0 2 0 2 1

[39,] 1 0 2 1 0 2

[40,] 1 0 2 1 2 0

[41,] 1 0 2 2 0 1

[42,] 1 0 2 2 1 0

[43,] 1 1 0 0 2 2

[44,] 1 1 0 2 0 2

[45,] 1 1 0 2 2 0

[46,] 1 1 2 0 0 2

[47,] 1 1 2 0 2 0

[48,] 1 1 2 2 0 0

[49,] 1 2 0 0 1 2

[50,] 1 2 0 0 2 1

[51,] 1 2 0 1 0 2

[52,] 1 2 0 1 2 0

[53,] 1 2 0 2 0 1

[54,] 1 2

Best Answer

Try this

x = [0 0 1 1 2 2];
M = unique(perms(x), 'rows');

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Answer 1

Try this

x = [0 0 1 1 2 2];
M = unique(perms(x), 'rows');