Identifier
- St000020: Permutations ⟶ ℤ
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
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Description
The rank of the permutation.
This is its position among all permutations of the same size ordered lexicographically.
This can be computed using the Lehmer code of a permutation:
$$\text{rank}(\sigma) = 1 +\sum_{i=1}^{n-1} L(\sigma)_i (n − i)!,$$
where $L(\sigma)_i$ is the $i$-th entry of the Lehmer code of $\sigma$.
This is its position among all permutations of the same size ordered lexicographically.
This can be computed using the Lehmer code of a permutation:
$$\text{rank}(\sigma) = 1 +\sum_{i=1}^{n-1} L(\sigma)_i (n − i)!,$$
where $L(\sigma)_i$ is the $i$-th entry of the Lehmer code of $\sigma$.
Code
def statistic(x):
return x.rank()+1
Created
Oct 01, 2011 at 20:56 by Chris Berg
Updated
Jun 28, 2022 at 16:25 by Nadia Lafreniere
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