How to create permutations of multisets?

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Vasilis Chasiotis
Vasilis Chasiotis 2020-5-16
编辑： Ameer Hamza 2020-5-16
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 0 2 1 0
[55,] 1 2 1 0 0 2
[56,] 1 2 1 0 2 0
[57,] 1 2 1 2 0 0
[58,] 1 2 2 0 0 1
[59,] 1 2 2 0 1 0
[60,] 1 2 2 1 0 0
[61,] 2 0 0 1 1 2
[62,] 2 0 0 1 2 1
[63,] 2 0 0 2 1 1
[64,] 2 0 1 0 1 2
[65,] 2 0 1 0 2 1
[66,] 2 0 1 1 0 2
[67,] 2 0 1 1 2 0
[68,] 2 0 1 2 0 1
[69,] 2 0 1 2 1 0
[70,] 2 0 2 0 1 1
[71,] 2 0 2 1 0 1
[72,] 2 0 2 1 1 0
[73,] 2 1 0 0 1 2
[74,] 2 1 0 0 2 1
[75,] 2 1 0 1 0 2
[76,] 2 1 0 1 2 0
[77,] 2 1 0 2 0 1
[78,] 2 1 0 2 1 0
[79,] 2 1 1 0 0 2
[80,] 2 1 1 0 2 0
[81,] 2 1 1 2 0 0
[82,] 2 1 2 0 0 1
[83,] 2 1 2 0 1 0
[84,] 2 1 2 1 0 0
[85,] 2 2 0 0 1 1
[86,] 2 2 0 1 0 1
[87,] 2 2 0 1 1 0
[88,] 2 2 1 0 0 1
[89,] 2 2 1 0 1 0
[90,] 2 2 1 1 0 0

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采纳的回答

Ameer Hamza
Ameer Hamza 2020-5-16
编辑：Ameer Hamza 2020-5-16
Try this
x = [0 0 1 1 2 2];
M = unique(perms(x), 'rows');

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