Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
St000001: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>1
[1,0,1,0]=>[2,1]=>1
[1,1,0,0]=>[1,2]=>1
[1,0,1,0,1,0]=>[3,2,1]=>2
[1,0,1,1,0,0]=>[2,3,1]=>1
[1,1,0,0,1,0]=>[3,1,2]=>1
[1,1,0,1,0,0]=>[2,1,3]=>1
[1,1,1,0,0,0]=>[1,2,3]=>1
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>16
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>5
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>6
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>3
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>1
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>5
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>2
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>3
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>2
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>1
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>1
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>1
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>1
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>1
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>768
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>168
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>216
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>70
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>14
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>216
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>56
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>90
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>35
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>9
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>20
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>10
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>4
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>1
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>168
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>42
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>56
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>21
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>5
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>70
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>21
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>35
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>16
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>5
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>10
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>6
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>3
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>1
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>14
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>5
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>9
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>5
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>2
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>4
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>3
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>2
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>1
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>1
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>1
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>1
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>1
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>292864
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>48048
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>64064
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>15015
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>2112
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>68640
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>12870
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>21450
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>5775
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>990
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>3520
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>1155
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>288
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>42
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>64064
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>11583
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>16016
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>4158
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>660
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>21450
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>4455
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>7700
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>2310
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>450
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>1540
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>567
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>162
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>28
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>3520
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>825
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>1540
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>525
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>120
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>448
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>189
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>64
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>14
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>70
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>35
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>15
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>48048
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>8580
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>11583
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>2970
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>462
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>12870
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>2640
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>4455
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>1320
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>252
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>825
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>300
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>84
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>14
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>15015
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>2970
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>4158
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>1188
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>210
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>5775
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>1320
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>2310
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>768
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>168
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>525
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>216
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>70
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>14
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>1155
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>300
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>567
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>216
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>56
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>189
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>90
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>35
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>35
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>20
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>10
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>2112
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>462
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>660
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>210
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>42
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>990
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>252
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>450
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>168
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>42
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>120
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>56
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>21
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>288
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>84
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>162
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>70
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>21
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>64
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>35
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>16
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>5
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>15
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>10
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>42
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>14
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>28
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>14
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>5
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>14
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>5
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>5
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>90
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>315
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>48
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>225
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>350
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>105
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>20
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>126
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>56
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>21
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>6534528
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>1361360
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>42
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>292864
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>48048
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>15015
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>2112
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>68640
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>21450
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>5775
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>990
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>3520
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>7700
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>2310
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>1540
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>126
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>972400
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>171600
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>50050
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>15015
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>3432
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>21450
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>2640
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>768
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>350
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>56
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>30030
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>9009
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>462
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>42
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>225
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>315
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>105
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>16
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>21
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>132
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>42
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>90
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>14
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>48
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>20
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>1
[]=>[]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>1
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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