Identifier
Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 4
[3,1,2] => 5
[3,2,1] => 6
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 5
[1,4,3,2] => 6
[2,1,3,4] => 7
[2,1,4,3] => 8
[2,3,1,4] => 9
[2,3,4,1] => 10
[2,4,1,3] => 11
[2,4,3,1] => 12
[3,1,2,4] => 13
[3,1,4,2] => 14
[3,2,1,4] => 15
[3,2,4,1] => 16
[3,4,1,2] => 17
[3,4,2,1] => 18
[4,1,2,3] => 19
[4,1,3,2] => 20
[4,2,1,3] => 21
[4,2,3,1] => 22
[4,3,1,2] => 23
[4,3,2,1] => 24
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 5
[1,2,5,4,3] => 6
[1,3,2,4,5] => 7
[1,3,2,5,4] => 8
[1,3,4,2,5] => 9
[1,3,4,5,2] => 10
[1,3,5,2,4] => 11
[1,3,5,4,2] => 12
[1,4,2,3,5] => 13
[1,4,2,5,3] => 14
[1,4,3,2,5] => 15
[1,4,3,5,2] => 16
[1,4,5,2,3] => 17
[1,4,5,3,2] => 18
[1,5,2,3,4] => 19
[1,5,2,4,3] => 20
[1,5,3,2,4] => 21
[1,5,3,4,2] => 22
[1,5,4,2,3] => 23
[1,5,4,3,2] => 24
[2,1,3,4,5] => 25
[2,1,3,5,4] => 26
[2,1,4,3,5] => 27
[2,1,4,5,3] => 28
[2,1,5,3,4] => 29
[2,1,5,4,3] => 30
[2,3,1,4,5] => 31
[2,3,1,5,4] => 32
[2,3,4,1,5] => 33
[2,3,4,5,1] => 34
[2,3,5,1,4] => 35
[2,3,5,4,1] => 36
[2,4,1,3,5] => 37
[2,4,1,5,3] => 38
[2,4,3,1,5] => 39
[2,4,3,5,1] => 40
[2,4,5,1,3] => 41
[2,4,5,3,1] => 42
[2,5,1,3,4] => 43
[2,5,1,4,3] => 44
[2,5,3,1,4] => 45
[2,5,3,4,1] => 46
[2,5,4,1,3] => 47
[2,5,4,3,1] => 48
[3,1,2,4,5] => 49
[3,1,2,5,4] => 50
[3,1,4,2,5] => 51
[3,1,4,5,2] => 52
[3,1,5,2,4] => 53
[3,1,5,4,2] => 54
[3,2,1,4,5] => 55
[3,2,1,5,4] => 56
[3,2,4,1,5] => 57
[3,2,4,5,1] => 58
[3,2,5,1,4] => 59
[3,2,5,4,1] => 60
[3,4,1,2,5] => 61
[3,4,1,5,2] => 62
[3,4,2,1,5] => 63
[3,4,2,5,1] => 64
[3,4,5,1,2] => 65
[3,4,5,2,1] => 66
[3,5,1,2,4] => 67
[3,5,1,4,2] => 68
[3,5,2,1,4] => 69
[3,5,2,4,1] => 70
[3,5,4,1,2] => 71
[3,5,4,2,1] => 72
[4,1,2,3,5] => 73
[4,1,2,5,3] => 74
[4,1,3,2,5] => 75
[4,1,3,5,2] => 76
[4,1,5,2,3] => 77
[4,1,5,3,2] => 78
[4,2,1,3,5] => 79
[4,2,1,5,3] => 80
[4,2,3,1,5] => 81
[4,2,3,5,1] => 82
[4,2,5,1,3] => 83
[4,2,5,3,1] => 84
[4,3,1,2,5] => 85
[4,3,1,5,2] => 86
[4,3,2,1,5] => 87
[4,3,2,5,1] => 88
[4,3,5,1,2] => 89
[4,3,5,2,1] => 90
[4,5,1,2,3] => 91
[4,5,1,3,2] => 92
[4,5,2,1,3] => 93
[4,5,2,3,1] => 94
[4,5,3,1,2] => 95
[4,5,3,2,1] => 96
[5,1,2,3,4] => 97
[5,1,2,4,3] => 98
[5,1,3,2,4] => 99
[5,1,3,4,2] => 100
[5,1,4,2,3] => 101
[5,1,4,3,2] => 102
[5,2,1,3,4] => 103
[5,2,1,4,3] => 104
[5,2,3,1,4] => 105
[5,2,3,4,1] => 106
[5,2,4,1,3] => 107
[5,2,4,3,1] => 108
[5,3,1,2,4] => 109
[5,3,1,4,2] => 110
[5,3,2,1,4] => 111
[5,3,2,4,1] => 112
[5,3,4,1,2] => 113
[5,3,4,2,1] => 114
[5,4,1,2,3] => 115
[5,4,1,3,2] => 116
[5,4,2,1,3] => 117
[5,4,2,3,1] => 118
[5,4,3,1,2] => 119
[5,4,3,2,1] => 120
[1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => 2
[1,2,3,5,4,6] => 3
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 7
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 9
[1,2,4,5,6,3] => 10
[1,2,4,6,3,5] => 11
[1,2,4,6,5,3] => 12
[1,2,5,3,4,6] => 13
[1,2,5,3,6,4] => 14
[1,2,5,4,3,6] => 15
[1,2,5,4,6,3] => 16
[1,2,5,6,3,4] => 17
[1,2,5,6,4,3] => 18
[1,2,6,3,4,5] => 19
[1,2,6,3,5,4] => 20
[1,2,6,4,3,5] => 21
[1,2,6,4,5,3] => 22
[1,2,6,5,3,4] => 23
[1,2,6,5,4,3] => 24
[1,3,2,4,5,6] => 25
[1,3,2,4,6,5] => 26
[1,3,2,5,4,6] => 27
[1,3,2,5,6,4] => 28
[1,3,2,6,4,5] => 29
[1,3,2,6,5,4] => 30
[1,3,4,2,5,6] => 31
[1,3,4,2,6,5] => 32
[1,3,4,5,2,6] => 33
[1,3,4,5,6,2] => 34
[1,3,4,6,2,5] => 35
[1,3,4,6,5,2] => 36
[1,3,5,2,4,6] => 37
[1,3,5,2,6,4] => 38
[1,3,5,4,2,6] => 39
[1,3,5,4,6,2] => 40
[1,3,5,6,2,4] => 41
[1,3,5,6,4,2] => 42
[1,3,6,2,4,5] => 43
[1,3,6,2,5,4] => 44
[1,3,6,4,2,5] => 45
[1,3,6,4,5,2] => 46
[1,3,6,5,2,4] => 47
[1,3,6,5,4,2] => 48
[1,4,2,3,5,6] => 49
[1,4,2,3,6,5] => 50
[1,4,2,5,3,6] => 51
[1,4,2,5,6,3] => 52
[1,4,2,6,3,5] => 53
[1,4,2,6,5,3] => 54
[1,4,3,2,5,6] => 55
[1,4,3,2,6,5] => 56
[1,4,3,5,2,6] => 57
[1,4,3,5,6,2] => 58
[1,4,3,6,2,5] => 59
[1,4,3,6,5,2] => 60
[1,4,5,2,3,6] => 61
[1,4,5,2,6,3] => 62
[1,4,5,3,2,6] => 63
[1,4,5,3,6,2] => 64
[1,4,5,6,2,3] => 65
[1,4,5,6,3,2] => 66
[1,4,6,2,3,5] => 67
[1,4,6,2,5,3] => 68
[1,4,6,3,2,5] => 69
[1,4,6,3,5,2] => 70
[1,4,6,5,2,3] => 71
[1,4,6,5,3,2] => 72
[1,5,2,3,4,6] => 73
[1,5,2,3,6,4] => 74
[1,5,2,4,3,6] => 75
[1,5,2,4,6,3] => 76
[1,5,2,6,3,4] => 77
[1,5,2,6,4,3] => 78
[1,5,3,2,4,6] => 79
[1,5,3,2,6,4] => 80
[1,5,3,4,2,6] => 81
[1,5,3,4,6,2] => 82
[1,5,3,6,2,4] => 83
[1,5,3,6,4,2] => 84
[1,5,4,2,3,6] => 85
[1,5,4,2,6,3] => 86
[1,5,4,3,2,6] => 87
[1,5,4,3,6,2] => 88
[1,5,4,6,2,3] => 89
[1,5,4,6,3,2] => 90
[1,5,6,2,3,4] => 91
[1,5,6,2,4,3] => 92
[1,5,6,3,2,4] => 93
[1,5,6,3,4,2] => 94
[1,5,6,4,2,3] => 95
[1,5,6,4,3,2] => 96
[1,6,2,3,4,5] => 97
[1,6,2,3,5,4] => 98
[1,6,2,4,3,5] => 99
[1,6,2,4,5,3] => 100
[1,6,2,5,3,4] => 101
[1,6,2,5,4,3] => 102
[1,6,3,2,4,5] => 103
[1,6,3,2,5,4] => 104
[1,6,3,4,2,5] => 105
[1,6,3,4,5,2] => 106
[1,6,3,5,2,4] => 107
[1,6,3,5,4,2] => 108
[1,6,4,2,3,5] => 109
[1,6,4,2,5,3] => 110
[1,6,4,3,2,5] => 111
[1,6,4,3,5,2] => 112
[1,6,4,5,2,3] => 113
[1,6,4,5,3,2] => 114
[1,6,5,2,3,4] => 115
[1,6,5,2,4,3] => 116
[1,6,5,3,2,4] => 117
[1,6,5,3,4,2] => 118
[1,6,5,4,2,3] => 119
[1,6,5,4,3,2] => 120
[2,1,3,4,5,6] => 121
[2,1,3,4,6,5] => 122
[2,1,3,5,4,6] => 123
[2,1,3,5,6,4] => 124
[2,1,3,6,4,5] => 125
[2,1,3,6,5,4] => 126
[2,1,4,3,5,6] => 127
[2,1,4,3,6,5] => 128
[2,1,4,5,3,6] => 129
[2,1,4,5,6,3] => 130
[2,1,4,6,3,5] => 131
[2,1,4,6,5,3] => 132
[2,1,5,3,4,6] => 133
[2,1,5,3,6,4] => 134
[2,1,5,4,3,6] => 135
[2,1,5,4,6,3] => 136
[2,1,5,6,3,4] => 137
[2,1,5,6,4,3] => 138
[2,1,6,3,4,5] => 139
[2,1,6,3,5,4] => 140
[2,1,6,4,3,5] => 141
[2,1,6,4,5,3] => 142
[2,1,6,5,3,4] => 143
[2,1,6,5,4,3] => 144
[2,3,1,4,5,6] => 145
[2,3,1,4,6,5] => 146
[2,3,1,5,4,6] => 147
[2,3,1,5,6,4] => 148
[2,3,1,6,4,5] => 149
[2,3,1,6,5,4] => 150
[2,3,4,1,5,6] => 151
[2,3,4,1,6,5] => 152
[2,3,4,5,1,6] => 153
[2,3,4,5,6,1] => 154
[2,3,4,6,1,5] => 155
[2,3,4,6,5,1] => 156
[2,3,5,1,4,6] => 157
[2,3,5,1,6,4] => 158
[2,3,5,4,1,6] => 159
[2,3,5,4,6,1] => 160
[2,3,5,6,1,4] => 161
[2,3,5,6,4,1] => 162
[2,3,6,1,4,5] => 163
[2,3,6,1,5,4] => 164
[2,3,6,4,1,5] => 165
[2,3,6,4,5,1] => 166
[2,3,6,5,1,4] => 167
[2,3,6,5,4,1] => 168
[2,4,1,3,5,6] => 169
[2,4,1,3,6,5] => 170
[2,4,1,5,3,6] => 171
[2,4,1,5,6,3] => 172
[2,4,1,6,3,5] => 173
[2,4,1,6,5,3] => 174
[2,4,3,1,5,6] => 175
[2,4,3,1,6,5] => 176
[2,4,3,5,1,6] => 177
[2,4,3,5,6,1] => 178
[2,4,3,6,1,5] => 179
[2,4,3,6,5,1] => 180
[2,4,5,1,3,6] => 181
[2,4,5,1,6,3] => 182
[2,4,5,3,1,6] => 183
[2,4,5,3,6,1] => 184
[2,4,5,6,1,3] => 185
[2,4,5,6,3,1] => 186
[2,4,6,1,3,5] => 187
[2,4,6,1,5,3] => 188
[2,4,6,3,1,5] => 189
[2,4,6,3,5,1] => 190
[2,4,6,5,1,3] => 191
[2,4,6,5,3,1] => 192
[2,5,1,3,4,6] => 193
[2,5,1,3,6,4] => 194
[2,5,1,4,3,6] => 195
[2,5,1,4,6,3] => 196
[2,5,1,6,3,4] => 197
[2,5,1,6,4,3] => 198
[2,5,3,1,4,6] => 199
[2,5,3,1,6,4] => 200
[2,5,3,4,1,6] => 201
[2,5,3,4,6,1] => 202
[2,5,3,6,1,4] => 203
[2,5,3,6,4,1] => 204
[2,5,4,1,3,6] => 205
[2,5,4,1,6,3] => 206
[2,5,4,3,1,6] => 207
[2,5,4,3,6,1] => 208
[2,5,4,6,1,3] => 209
[2,5,4,6,3,1] => 210
[2,5,6,1,3,4] => 211
[2,5,6,1,4,3] => 212
[2,5,6,3,1,4] => 213
[2,5,6,3,4,1] => 214
[2,5,6,4,1,3] => 215
[2,5,6,4,3,1] => 216
[2,6,1,3,4,5] => 217
[2,6,1,3,5,4] => 218
[2,6,1,4,3,5] => 219
[2,6,1,4,5,3] => 220
[2,6,1,5,3,4] => 221
[2,6,1,5,4,3] => 222
[2,6,3,1,4,5] => 223
[2,6,3,1,5,4] => 224
[2,6,3,4,1,5] => 225
[2,6,3,4,5,1] => 226
[2,6,3,5,1,4] => 227
[2,6,3,5,4,1] => 228
[2,6,4,1,3,5] => 229
[2,6,4,1,5,3] => 230
[2,6,4,3,1,5] => 231
[2,6,4,3,5,1] => 232
[2,6,4,5,1,3] => 233
[2,6,4,5,3,1] => 234
[2,6,5,1,3,4] => 235
[2,6,5,1,4,3] => 236
[2,6,5,3,1,4] => 237
[2,6,5,3,4,1] => 238
[2,6,5,4,1,3] => 239
[2,6,5,4,3,1] => 240
[3,1,2,4,5,6] => 241
[3,1,2,4,6,5] => 242
[3,1,2,5,4,6] => 243
[3,1,2,5,6,4] => 244
[3,1,2,6,4,5] => 245
[3,1,2,6,5,4] => 246
[3,1,4,2,5,6] => 247
[3,1,4,2,6,5] => 248
[3,1,4,5,2,6] => 249
[3,1,4,5,6,2] => 250
[3,1,4,6,2,5] => 251
[3,1,4,6,5,2] => 252
[3,1,5,2,4,6] => 253
[3,1,5,2,6,4] => 254
[3,1,5,4,2,6] => 255
[3,1,5,4,6,2] => 256
[3,1,5,6,2,4] => 257
[3,1,5,6,4,2] => 258
[3,1,6,2,4,5] => 259
[3,1,6,2,5,4] => 260
[3,1,6,4,2,5] => 261
[3,1,6,4,5,2] => 262
[3,1,6,5,2,4] => 263
[3,1,6,5,4,2] => 264
[3,2,1,4,5,6] => 265
[3,2,1,4,6,5] => 266
[3,2,1,5,4,6] => 267
[3,2,1,5,6,4] => 268
[3,2,1,6,4,5] => 269
[3,2,1,6,5,4] => 270
[3,2,4,1,5,6] => 271
[3,2,4,1,6,5] => 272
[3,2,4,5,1,6] => 273
[3,2,4,5,6,1] => 274
[3,2,4,6,1,5] => 275
[3,2,4,6,5,1] => 276
[3,2,5,1,4,6] => 277
[3,2,5,1,6,4] => 278
[3,2,5,4,1,6] => 279
[3,2,5,4,6,1] => 280
[3,2,5,6,1,4] => 281
[3,2,5,6,4,1] => 282
[3,2,6,1,4,5] => 283
[3,2,6,1,5,4] => 284
[3,2,6,4,1,5] => 285
[3,2,6,4,5,1] => 286
[3,2,6,5,1,4] => 287
[3,2,6,5,4,1] => 288
[3,4,1,2,5,6] => 289
[3,4,1,2,6,5] => 290
[3,4,1,5,2,6] => 291
[3,4,1,5,6,2] => 292
[3,4,1,6,2,5] => 293
[3,4,1,6,5,2] => 294
[3,4,2,1,5,6] => 295
[3,4,2,1,6,5] => 296
[3,4,2,5,1,6] => 297
[3,4,2,5,6,1] => 298
[3,4,2,6,1,5] => 299
[3,4,2,6,5,1] => 300
[3,4,5,1,2,6] => 301
[3,4,5,1,6,2] => 302
[3,4,5,2,1,6] => 303
[3,4,5,2,6,1] => 304
[3,4,5,6,1,2] => 305
[3,4,5,6,2,1] => 306
[3,4,6,1,2,5] => 307
[3,4,6,1,5,2] => 308
[3,4,6,2,1,5] => 309
[3,4,6,2,5,1] => 310
[3,4,6,5,1,2] => 311
[3,4,6,5,2,1] => 312
[3,5,1,2,4,6] => 313
[3,5,1,2,6,4] => 314
[3,5,1,4,2,6] => 315
[3,5,1,4,6,2] => 316
[3,5,1,6,2,4] => 317
[3,5,1,6,4,2] => 318
[3,5,2,1,4,6] => 319
[3,5,2,1,6,4] => 320
[3,5,2,4,1,6] => 321
[3,5,2,4,6,1] => 322
[3,5,2,6,1,4] => 323
[3,5,2,6,4,1] => 324
[3,5,4,1,2,6] => 325
[3,5,4,1,6,2] => 326
[3,5,4,2,1,6] => 327
[3,5,4,2,6,1] => 328
[3,5,4,6,1,2] => 329
[3,5,4,6,2,1] => 330
[3,5,6,1,2,4] => 331
[3,5,6,1,4,2] => 332
[3,5,6,2,1,4] => 333
[3,5,6,2,4,1] => 334
[3,5,6,4,1,2] => 335
[3,5,6,4,2,1] => 336
[3,6,1,2,4,5] => 337
[3,6,1,2,5,4] => 338
[3,6,1,4,2,5] => 339
[3,6,1,4,5,2] => 340
[3,6,1,5,2,4] => 341
[3,6,1,5,4,2] => 342
[3,6,2,1,4,5] => 343
[3,6,2,1,5,4] => 344
[3,6,2,4,1,5] => 345
[3,6,2,4,5,1] => 346
[3,6,2,5,1,4] => 347
[3,6,2,5,4,1] => 348
[3,6,4,1,2,5] => 349
[3,6,4,1,5,2] => 350
[3,6,4,2,1,5] => 351
[3,6,4,2,5,1] => 352
[3,6,4,5,1,2] => 353
[3,6,4,5,2,1] => 354
[3,6,5,1,2,4] => 355
[3,6,5,1,4,2] => 356
[3,6,5,2,1,4] => 357
[3,6,5,2,4,1] => 358
[3,6,5,4,1,2] => 359
[3,6,5,4,2,1] => 360
[4,1,2,3,5,6] => 361
[4,1,2,3,6,5] => 362
[4,1,2,5,3,6] => 363
[4,1,2,5,6,3] => 364
[4,1,2,6,3,5] => 365
[4,1,2,6,5,3] => 366
[4,1,3,2,5,6] => 367
[4,1,3,2,6,5] => 368
[4,1,3,5,2,6] => 369
[4,1,3,5,6,2] => 370
[4,1,3,6,2,5] => 371
[4,1,3,6,5,2] => 372
[4,1,5,2,3,6] => 373
[4,1,5,2,6,3] => 374
[4,1,5,3,2,6] => 375
[4,1,5,3,6,2] => 376
[4,1,5,6,2,3] => 377
[4,1,5,6,3,2] => 378
[4,1,6,2,3,5] => 379
[4,1,6,2,5,3] => 380
[4,1,6,3,2,5] => 381
[4,1,6,3,5,2] => 382
[4,1,6,5,2,3] => 383
[4,1,6,5,3,2] => 384
[4,2,1,3,5,6] => 385
[4,2,1,3,6,5] => 386
[4,2,1,5,3,6] => 387
[4,2,1,5,6,3] => 388
[4,2,1,6,3,5] => 389
[4,2,1,6,5,3] => 390
[4,2,3,1,5,6] => 391
[4,2,3,1,6,5] => 392
[4,2,3,5,1,6] => 393
[4,2,3,5,6,1] => 394
[4,2,3,6,1,5] => 395
[4,2,3,6,5,1] => 396
[4,2,5,1,3,6] => 397
[4,2,5,1,6,3] => 398
[4,2,5,3,1,6] => 399
[4,2,5,3,6,1] => 400
[4,2,5,6,1,3] => 401
[4,2,5,6,3,1] => 402
[4,2,6,1,3,5] => 403
[4,2,6,1,5,3] => 404
[4,2,6,3,1,5] => 405
[4,2,6,3,5,1] => 406
[4,2,6,5,1,3] => 407
[4,2,6,5,3,1] => 408
[4,3,1,2,5,6] => 409
[4,3,1,2,6,5] => 410
[4,3,1,5,2,6] => 411
[4,3,1,5,6,2] => 412
[4,3,1,6,2,5] => 413
[4,3,1,6,5,2] => 414
[4,3,2,1,5,6] => 415
[4,3,2,1,6,5] => 416
[4,3,2,5,1,6] => 417
[4,3,2,5,6,1] => 418
[4,3,2,6,1,5] => 419
[4,3,2,6,5,1] => 420
[4,3,5,1,2,6] => 421
[4,3,5,1,6,2] => 422
[4,3,5,2,1,6] => 423
[4,3,5,2,6,1] => 424
[4,3,5,6,1,2] => 425
[4,3,5,6,2,1] => 426
[4,3,6,1,2,5] => 427
[4,3,6,1,5,2] => 428
[4,3,6,2,1,5] => 429
[4,3,6,2,5,1] => 430
[4,3,6,5,1,2] => 431
[4,3,6,5,2,1] => 432
[4,5,1,2,3,6] => 433
[4,5,1,2,6,3] => 434
[4,5,1,3,2,6] => 435
[4,5,1,3,6,2] => 436
[4,5,1,6,2,3] => 437
[4,5,1,6,3,2] => 438
[4,5,2,1,3,6] => 439
[4,5,2,1,6,3] => 440
[4,5,2,3,1,6] => 441
[4,5,2,3,6,1] => 442
[4,5,2,6,1,3] => 443
[4,5,2,6,3,1] => 444
[4,5,3,1,2,6] => 445
[4,5,3,1,6,2] => 446
[4,5,3,2,1,6] => 447
[4,5,3,2,6,1] => 448
[4,5,3,6,1,2] => 449
[4,5,3,6,2,1] => 450
[4,5,6,1,2,3] => 451
[4,5,6,1,3,2] => 452
[4,5,6,2,1,3] => 453
[4,5,6,2,3,1] => 454
[4,5,6,3,1,2] => 455
[4,5,6,3,2,1] => 456
[4,6,1,2,3,5] => 457
[4,6,1,2,5,3] => 458
[4,6,1,3,2,5] => 459
[4,6,1,3,5,2] => 460
[4,6,1,5,2,3] => 461
[4,6,1,5,3,2] => 462
[4,6,2,1,3,5] => 463
[4,6,2,1,5,3] => 464
[4,6,2,3,1,5] => 465
[4,6,2,3,5,1] => 466
[4,6,2,5,1,3] => 467
[4,6,2,5,3,1] => 468
[4,6,3,1,2,5] => 469
[4,6,3,1,5,2] => 470
[4,6,3,2,1,5] => 471
[4,6,3,2,5,1] => 472
[4,6,3,5,1,2] => 473
[4,6,3,5,2,1] => 474
[4,6,5,1,2,3] => 475
[4,6,5,1,3,2] => 476
[4,6,5,2,1,3] => 477
[4,6,5,2,3,1] => 478
[4,6,5,3,1,2] => 479
[4,6,5,3,2,1] => 480
[5,1,2,3,4,6] => 481
[5,1,2,3,6,4] => 482
[5,1,2,4,3,6] => 483
[5,1,2,4,6,3] => 484
[5,1,2,6,3,4] => 485
[5,1,2,6,4,3] => 486
[5,1,3,2,4,6] => 487
[5,1,3,2,6,4] => 488
[5,1,3,4,2,6] => 489
[5,1,3,4,6,2] => 490
[5,1,3,6,2,4] => 491
[5,1,3,6,4,2] => 492
[5,1,4,2,3,6] => 493
[5,1,4,2,6,3] => 494
[5,1,4,3,2,6] => 495
[5,1,4,3,6,2] => 496
[5,1,4,6,2,3] => 497
[5,1,4,6,3,2] => 498
[5,1,6,2,3,4] => 499
[5,1,6,2,4,3] => 500
[5,1,6,3,2,4] => 501
[5,1,6,3,4,2] => 502
[5,1,6,4,2,3] => 503
[5,1,6,4,3,2] => 504
[5,2,1,3,4,6] => 505
[5,2,1,3,6,4] => 506
[5,2,1,4,3,6] => 507
[5,2,1,4,6,3] => 508
[5,2,1,6,3,4] => 509
[5,2,1,6,4,3] => 510
[5,2,3,1,4,6] => 511
[5,2,3,1,6,4] => 512
[5,2,3,4,1,6] => 513
[5,2,3,4,6,1] => 514
[5,2,3,6,1,4] => 515
[5,2,3,6,4,1] => 516
[5,2,4,1,3,6] => 517
[5,2,4,1,6,3] => 518
[5,2,4,3,1,6] => 519
[5,2,4,3,6,1] => 520
[5,2,4,6,1,3] => 521
[5,2,4,6,3,1] => 522
[5,2,6,1,3,4] => 523
[5,2,6,1,4,3] => 524
[5,2,6,3,1,4] => 525
[5,2,6,3,4,1] => 526
[5,2,6,4,1,3] => 527
[5,2,6,4,3,1] => 528
[5,3,1,2,4,6] => 529
[5,3,1,2,6,4] => 530
[5,3,1,4,2,6] => 531
[5,3,1,4,6,2] => 532
[5,3,1,6,2,4] => 533
[5,3,1,6,4,2] => 534
[5,3,2,1,4,6] => 535
[5,3,2,1,6,4] => 536
[5,3,2,4,1,6] => 537
[5,3,2,4,6,1] => 538
[5,3,2,6,1,4] => 539
[5,3,2,6,4,1] => 540
[5,3,4,1,2,6] => 541
[5,3,4,1,6,2] => 542
[5,3,4,2,1,6] => 543
[5,3,4,2,6,1] => 544
[5,3,4,6,1,2] => 545
[5,3,4,6,2,1] => 546
[5,3,6,1,2,4] => 547
[5,3,6,1,4,2] => 548
[5,3,6,2,1,4] => 549
[5,3,6,2,4,1] => 550
[5,3,6,4,1,2] => 551
[5,3,6,4,2,1] => 552
[5,4,1,2,3,6] => 553
[5,4,1,2,6,3] => 554
[5,4,1,3,2,6] => 555
[5,4,1,3,6,2] => 556
[5,4,1,6,2,3] => 557
[5,4,1,6,3,2] => 558
[5,4,2,1,3,6] => 559
[5,4,2,1,6,3] => 560
[5,4,2,3,1,6] => 561
[5,4,2,3,6,1] => 562
[5,4,2,6,1,3] => 563
[5,4,2,6,3,1] => 564
[5,4,3,1,2,6] => 565
[5,4,3,1,6,2] => 566
[5,4,3,2,1,6] => 567
[5,4,3,2,6,1] => 568
[5,4,3,6,1,2] => 569
[5,4,3,6,2,1] => 570
[5,4,6,1,2,3] => 571
[5,4,6,1,3,2] => 572
[5,4,6,2,1,3] => 573
[5,4,6,2,3,1] => 574
[5,4,6,3,1,2] => 575
[5,4,6,3,2,1] => 576
[5,6,1,2,3,4] => 577
[5,6,1,2,4,3] => 578
[5,6,1,3,2,4] => 579
[5,6,1,3,4,2] => 580
[5,6,1,4,2,3] => 581
[5,6,1,4,3,2] => 582
[5,6,2,1,3,4] => 583
[5,6,2,1,4,3] => 584
[5,6,2,3,1,4] => 585
[5,6,2,3,4,1] => 586
[5,6,2,4,1,3] => 587
[5,6,2,4,3,1] => 588
[5,6,3,1,2,4] => 589
[5,6,3,1,4,2] => 590
[5,6,3,2,1,4] => 591
[5,6,3,2,4,1] => 592
[5,6,3,4,1,2] => 593
[5,6,3,4,2,1] => 594
[5,6,4,1,2,3] => 595
[5,6,4,1,3,2] => 596
[5,6,4,2,1,3] => 597
[5,6,4,2,3,1] => 598
[5,6,4,3,1,2] => 599
[5,6,4,3,2,1] => 600
[6,1,2,3,4,5] => 601
[6,1,2,3,5,4] => 602
[6,1,2,4,3,5] => 603
[6,1,2,4,5,3] => 604
[6,1,2,5,3,4] => 605
[6,1,2,5,4,3] => 606
[6,1,3,2,4,5] => 607
[6,1,3,2,5,4] => 608
[6,1,3,4,2,5] => 609
[6,1,3,4,5,2] => 610
[6,1,3,5,2,4] => 611
[6,1,3,5,4,2] => 612
[6,1,4,2,3,5] => 613
[6,1,4,2,5,3] => 614
[6,1,4,3,2,5] => 615
[6,1,4,3,5,2] => 616
[6,1,4,5,2,3] => 617
[6,1,4,5,3,2] => 618
[6,1,5,2,3,4] => 619
[6,1,5,2,4,3] => 620
[6,1,5,3,2,4] => 621
[6,1,5,3,4,2] => 622
[6,1,5,4,2,3] => 623
[6,1,5,4,3,2] => 624
[6,2,1,3,4,5] => 625
[6,2,1,3,5,4] => 626
[6,2,1,4,3,5] => 627
[6,2,1,4,5,3] => 628
[6,2,1,5,3,4] => 629
[6,2,1,5,4,3] => 630
[6,2,3,1,4,5] => 631
[6,2,3,1,5,4] => 632
[6,2,3,4,1,5] => 633
[6,2,3,4,5,1] => 634
[6,2,3,5,1,4] => 635
[6,2,3,5,4,1] => 636
[6,2,4,1,3,5] => 637
[6,2,4,1,5,3] => 638
[6,2,4,3,1,5] => 639
[6,2,4,3,5,1] => 640
[6,2,4,5,1,3] => 641
[6,2,4,5,3,1] => 642
[6,2,5,1,3,4] => 643
[6,2,5,1,4,3] => 644
[6,2,5,3,1,4] => 645
[6,2,5,3,4,1] => 646
[6,2,5,4,1,3] => 647
[6,2,5,4,3,1] => 648
[6,3,1,2,4,5] => 649
[6,3,1,2,5,4] => 650
[6,3,1,4,2,5] => 651
[6,3,1,4,5,2] => 652
[6,3,1,5,2,4] => 653
[6,3,1,5,4,2] => 654
[6,3,2,1,4,5] => 655
[6,3,2,1,5,4] => 656
[6,3,2,4,1,5] => 657
[6,3,2,4,5,1] => 658
[6,3,2,5,1,4] => 659
[6,3,2,5,4,1] => 660
[6,3,4,1,2,5] => 661
[6,3,4,1,5,2] => 662
[6,3,4,2,1,5] => 663
[6,3,4,2,5,1] => 664
[6,3,4,5,1,2] => 665
[6,3,4,5,2,1] => 666
[6,3,5,1,2,4] => 667
[6,3,5,1,4,2] => 668
[6,3,5,2,1,4] => 669
[6,3,5,2,4,1] => 670
[6,3,5,4,1,2] => 671
[6,3,5,4,2,1] => 672
[6,4,1,2,3,5] => 673
[6,4,1,2,5,3] => 674
[6,4,1,3,2,5] => 675
[6,4,1,3,5,2] => 676
[6,4,1,5,2,3] => 677
[6,4,1,5,3,2] => 678
[6,4,2,1,3,5] => 679
[6,4,2,1,5,3] => 680
[6,4,2,3,1,5] => 681
[6,4,2,3,5,1] => 682
[6,4,2,5,1,3] => 683
[6,4,2,5,3,1] => 684
[6,4,3,1,2,5] => 685
[6,4,3,1,5,2] => 686
[6,4,3,2,1,5] => 687
[6,4,3,2,5,1] => 688
[6,4,3,5,1,2] => 689
[6,4,3,5,2,1] => 690
[6,4,5,1,2,3] => 691
[6,4,5,1,3,2] => 692
[6,4,5,2,1,3] => 693
[6,4,5,2,3,1] => 694
[6,4,5,3,1,2] => 695
[6,4,5,3,2,1] => 696
[6,5,1,2,3,4] => 697
[6,5,1,2,4,3] => 698
[6,5,1,3,2,4] => 699
[6,5,1,3,4,2] => 700
[6,5,1,4,2,3] => 701
[6,5,1,4,3,2] => 702
[6,5,2,1,3,4] => 703
[6,5,2,1,4,3] => 704
[6,5,2,3,1,4] => 705
[6,5,2,3,4,1] => 706
[6,5,2,4,1,3] => 707
[6,5,2,4,3,1] => 708
[6,5,3,1,2,4] => 709
[6,5,3,1,4,2] => 710
[6,5,3,2,1,4] => 711
[6,5,3,2,4,1] => 712
[6,5,3,4,1,2] => 713
[6,5,3,4,2,1] => 714
[6,5,4,1,2,3] => 715
[6,5,4,1,3,2] => 716
[6,5,4,2,1,3] => 717
[6,5,4,2,3,1] => 718
[6,5,4,3,1,2] => 719
[6,5,4,3,2,1] => 720
click to show generating function       
Description
The rank of the permutation.
This is its position among all permutations of the same size ordered lexicographically.
Code
def statistic(x):
    return x.rank()+1
Created
Oct 01, 2011 at 20:56 by Chris Berg
Updated
Sep 12, 2014 at 20:25 by Martin Rubey