Template:Schoute permutation/python example

examples with degree 4 (Python code)

This code uses the Python library discrete helpers.

import numpy as np

from discretehelpers.a import int_to_perm


perm_matrix = np.zeros([24, 4], dtype=int)
schoute_matrix = np.zeros([24, 16], dtype=int)

for i in range(24):
    perm_object = int_to_perm(i)

    perm_matrix[i, :] = perm_object.sequence(4)
    schoute_matrix[i, :] = perm_object.schoute_perm.sequence(16)

n

n-th finite permutation

n-th Schoute permutation

[[0, 1, 2, 3],
 [1, 0, 2, 3],
 [0, 2, 1, 3],
 [2, 0, 1, 3],
 [1, 2, 0, 3],
 [2, 1, 0, 3],

 [0, 1, 3, 2],
 [1, 0, 3, 2],
 [0, 3, 1, 2],
 [3, 0, 1, 2],
 [1, 3, 0, 2],
 [3, 1, 0, 2],

 [0, 2, 3, 1],
 [2, 0, 3, 1],
 [0, 3, 2, 1],
 [3, 0, 2, 1],
 [2, 3, 0, 1],
 [3, 2, 0, 1],

 [1, 2, 3, 0],
 [2, 1, 3, 0],
 [1, 3, 2, 0],
 [3, 1, 2, 0],
 [2, 3, 1, 0],
 [3, 2, 1, 0]]

[[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15],
 [ 0,  2,  1,  3,  4,  6,  5,  7,  8, 10,  9, 11, 12, 14, 13, 15],
 [ 0,  1,  4,  5,  2,  3,  6,  7,  8,  9, 12, 13, 10, 11, 14, 15],
 [ 0,  4,  1,  5,  2,  6,  3,  7,  8, 12,  9, 13, 10, 14, 11, 15],
 [ 0,  2,  4,  6,  1,  3,  5,  7,  8, 10, 12, 14,  9, 11, 13, 15],
 [ 0,  4,  2,  6,  1,  5,  3,  7,  8, 12, 10, 14,  9, 13, 11, 15],

 [ 0,  1,  2,  3,  8,  9, 10, 11,  4,  5,  6,  7, 12, 13, 14, 15],
 [ 0,  2,  1,  3,  8, 10,  9, 11,  4,  6,  5,  7, 12, 14, 13, 15],
 [ 0,  1,  8,  9,  2,  3, 10, 11,  4,  5, 12, 13,  6,  7, 14, 15],
 [ 0,  8,  1,  9,  2, 10,  3, 11,  4, 12,  5, 13,  6, 14,  7, 15],
 [ 0,  2,  8, 10,  1,  3,  9, 11,  4,  6, 12, 14,  5,  7, 13, 15],
 [ 0,  8,  2, 10,  1,  9,  3, 11,  4, 12,  6, 14,  5, 13,  7, 15],

 [ 0,  1,  4,  5,  8,  9, 12, 13,  2,  3,  6,  7, 10, 11, 14, 15],
 [ 0,  4,  1,  5,  8, 12,  9, 13,  2,  6,  3,  7, 10, 14, 11, 15],
 [ 0,  1,  8,  9,  4,  5, 12, 13,  2,  3, 10, 11,  6,  7, 14, 15],
 [ 0,  8,  1,  9,  4, 12,  5, 13,  2, 10,  3, 11,  6, 14,  7, 15],
 [ 0,  4,  8, 12,  1,  5,  9, 13,  2,  6, 10, 14,  3,  7, 11, 15],
 [ 0,  8,  4, 12,  1,  9,  5, 13,  2, 10,  6, 14,  3, 11,  7, 15],

 [ 0,  2,  4,  6,  8, 10, 12, 14,  1,  3,  5,  7,  9, 11, 13, 15],
 [ 0,  4,  2,  6,  8, 12, 10, 14,  1,  5,  3,  7,  9, 13, 11, 15],
 [ 0,  2,  8, 10,  4,  6, 12, 14,  1,  3,  9, 11,  5,  7, 13, 15],
 [ 0,  8,  2, 10,  4, 12,  6, 14,  1,  9,  3, 11,  5, 13,  7, 15],
 [ 0,  4,  8, 12,  2,  6, 10, 14,  1,  5,  9, 13,  3,  7, 11, 15],
 [ 0,  8,  4, 12,  2, 10,  6, 14,  1,  9,  5, 13,  3, 11,  7, 15]]