- FindStat

Identifier

St001312: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,1]=>2
[2]=>1
[1,1,1]=>5
[1,2]=>3
[2,1]=>3
[3]=>1
[1,1,1,1]=>14
[1,1,2]=>9
[1,2,1]=>10
[1,3]=>4
[2,1,1]=>9
[2,2]=>6
[3,1]=>4
[4]=>1
[1,1,1,1,1]=>42
[1,1,1,2]=>28
[1,1,2,1]=>32
[1,1,3]=>14
[1,2,1,1]=>32
[1,2,2]=>22
[1,3,1]=>17
[1,4]=>5
[2,1,1,1]=>28
[2,1,2]=>19
[2,2,1]=>22
[2,3]=>10
[3,1,1]=>14
[3,2]=>10
[4,1]=>5
[5]=>1
[1,1,1,1,1,1]=>132
[1,1,1,1,2]=>90
[1,1,1,2,1]=>104
[1,1,1,3]=>48
[1,1,2,1,1]=>107
[1,1,2,2]=>75
[1,1,3,1]=>62
[1,1,4]=>20
[1,2,1,1,1]=>104
[1,2,1,2]=>72
[1,2,2,1]=>84
[1,2,3]=>40
[1,3,1,1]=>62
[1,3,2]=>45
[1,4,1]=>26
[1,5]=>6
[2,1,1,1,1]=>90
[2,1,1,2]=>62
[2,1,2,1]=>72
[2,1,3]=>34
[2,2,1,1]=>75
[2,2,2]=>53
[2,3,1]=>45
[2,4]=>15
[3,1,1,1]=>48
[3,1,2]=>34
[3,2,1]=>40
[3,3]=>20
[4,1,1]=>20
[4,2]=>15
[5,1]=>6
[6]=>1
[1,1,1,1,1,1,1]=>429
[1,1,1,1,1,2]=>297
[1,1,1,1,2,1]=>345
[1,1,1,1,3]=>165
[1,1,1,2,1,1]=>359
[1,1,1,2,2]=>255
[1,1,1,3,1]=>219
[1,1,1,4]=>75
[1,1,2,1,1,1]=>359
[1,1,2,1,2]=>252
[1,1,2,2,1]=>295
[1,1,2,3]=>145
[1,1,3,1,1]=>233
[1,1,3,2]=>171
[1,1,4,1]=>107
[1,1,5]=>27
[1,2,1,1,1,1]=>345
[1,2,1,1,2]=>241
[1,2,1,2,1]=>281
[1,2,1,3]=>137
[1,2,2,1,1]=>295
[1,2,2,2]=>211
[1,2,3,1]=>185
[1,2,4]=>65
[1,3,1,1,1]=>219
[1,3,1,2]=>157
[1,3,2,1]=>185
[1,3,3]=>95
[1,4,1,1]=>107
[1,4,2]=>81
[1,5,1]=>37
[1,6]=>7
[2,1,1,1,1,1]=>297
[2,1,1,1,2]=>207
[2,1,1,2,1]=>241
[2,1,1,3]=>117
[2,1,2,1,1]=>252
[2,1,2,2]=>180
[2,1,3,1]=>157
[2,1,4]=>55
[2,2,1,1,1]=>255
[2,2,1,2]=>180
[2,2,2,1]=>211
[2,2,3]=>105
[2,3,1,1]=>171
[2,3,2]=>126
[2,4,1]=>81
[2,5]=>21
[3,1,1,1,1]=>165
[3,1,1,2]=>117
[3,1,2,1]=>137
[3,1,3]=>69
[3,2,1,1]=>145
[3,2,2]=>105
[3,3,1]=>95
[3,4]=>35
[4,1,1,1]=>75
[4,1,2]=>55
[4,2,1]=>65
[4,3]=>35
[5,1,1]=>27
[5,2]=>21
[6,1]=>7
[7]=>1
[1,1,1,1,1,1,1,1]=>1430
[1,1,1,1,1,1,2]=>1001
[1,1,1,1,1,2,1]=>1166
[1,1,1,1,1,3]=>572
[1,1,1,1,2,1,1]=>1220
[1,1,1,1,2,2]=>875
[1,1,1,1,3,1]=>770
[1,1,1,1,4]=>275
[1,1,1,2,1,1,1]=>1234
[1,1,1,2,1,2]=>875
[1,1,1,2,2,1]=>1026
[1,1,1,2,3]=>516
[1,1,1,3,1,1]=>842
[1,1,1,3,2]=>623
[1,1,1,4,1]=>410
[1,1,1,5]=>110
[1,1,2,1,1,1,1]=>1220
[1,1,2,1,1,2]=>861
[1,1,2,1,2,1]=>1006
[1,1,2,1,3]=>502
[1,1,2,2,1,1]=>1060
[1,1,2,2,2]=>765
[1,1,2,3,1]=>685
[1,1,2,4]=>250
[1,1,3,1,1,1]=>842
[1,1,3,1,2]=>609
[1,1,3,2,1]=>718
[1,1,3,3]=>376
[1,1,4,1,1]=>450
[1,1,4,2]=>343
[1,1,5,1]=>170
[1,1,6]=>35
[1,2,1,1,1,1,1]=>1166
[1,2,1,1,1,2]=>821
[1,2,1,1,2,1]=>958
[1,2,1,1,3]=>476
[1,2,1,2,1,1]=>1006
[1,2,1,2,2]=>725
[1,2,1,3,1]=>646
[1,2,1,4]=>235
[1,2,2,1,1,1]=>1026
[1,2,2,1,2]=>731
[1,2,2,2,1]=>858
[1,2,2,3]=>436
[1,2,3,1,1]=>718
[1,2,3,2]=>533
[1,2,4,1]=>358
[1,2,5]=>98
[1,3,1,1,1,1]=>770
[1,3,1,1,2]=>551
[1,3,1,2,1]=>646
[1,3,1,3]=>332
[1,3,2,1,1]=>685
[1,3,2,2]=>500
[1,3,3,1]=>460
[1,3,4]=>175
[1,4,1,1,1]=>410
[1,4,1,2]=>303
[1,4,2,1]=>358
[1,4,3]=>196
[1,5,1,1]=>170
[1,5,2]=>133
[1,6,1]=>50
[1,7]=>8
[2,1,1,1,1,1,1]=>1001
[2,1,1,1,1,2]=>704
[2,1,1,1,2,1]=>821
[2,1,1,1,3]=>407
[2,1,1,2,1,1]=>861
[2,1,1,2,2]=>620
[2,1,1,3,1]=>551
[2,1,1,4]=>200
[2,1,2,1,1,1]=>875
[2,1,2,1,2]=>623
[2,1,2,2,1]=>731
[2,1,2,3]=>371
[2,1,3,1,1]=>609
[2,1,3,2]=>452
[2,1,4,1]=>303
[2,1,5]=>83
[2,2,1,1,1,1]=>875
[2,2,1,1,2]=>620
[2,2,1,2,1]=>725
[2,2,1,3]=>365
[2,2,2,1,1]=>765
[2,2,2,2]=>554
[2,2,3,1]=>500
[2,2,4]=>185
[2,3,1,1,1]=>623
[2,3,1,2]=>452
[2,3,2,1]=>533
[2,3,3]=>281
[2,4,1,1]=>343
[2,4,2]=>262
[2,5,1]=>133
[2,6]=>28
[3,1,1,1,1,1]=>572
[3,1,1,1,2]=>407
[3,1,1,2,1]=>476
[3,1,1,3]=>242
[3,1,2,1,1]=>502
[3,1,2,2]=>365
[3,1,3,1]=>332
[3,1,4]=>125
[3,2,1,1,1]=>516
[3,2,1,2]=>371
[3,2,2,1]=>436
[3,2,3]=>226
[3,3,1,1]=>376
[3,3,2]=>281
[3,4,1]=>196
[3,5]=>56
[4,1,1,1,1]=>275
[4,1,1,2]=>200
[4,1,2,1]=>235
[4,1,3]=>125
[4,2,1,1]=>250
[4,2,2]=>185
[4,3,1]=>175
[4,4]=>70
[5,1,1,1]=>110
[5,1,2]=>83
[5,2,1]=>98
[5,3]=>56
[6,1,1]=>35
[6,2]=>28
[7,1]=>8
[8]=>1
[1,1,1,1,1,1,1,1,1]=>4862
[1,1,1,1,1,1,1,2]=>3432
[1,1,1,1,1,1,2,1]=>4004
[1,1,1,1,1,1,3]=>2002
[1,1,1,1,1,2,1,1]=>4202
[1,1,1,1,1,2,2]=>3036
[1,1,1,1,1,3,1]=>2717
[1,1,1,1,1,4]=>1001
[1,1,1,1,2,1,1,1]=>4274
[1,1,1,1,2,1,2]=>3054
[1,1,1,1,2,2,1]=>3584
[1,1,1,1,2,3]=>1834
[1,1,1,1,3,1,1]=>3014
[1,1,1,1,3,2]=>2244
[1,1,1,1,4,1]=>1529
[1,1,1,1,5]=>429
[1,1,1,2,1,1,1,1]=>4274
[1,1,1,2,1,1,2]=>3040
[1,1,1,2,1,2,1]=>3556
[1,1,1,2,1,3]=>1806
[1,1,1,2,2,1,1]=>3754
[1,1,1,2,2,2]=>2728
[1,1,1,2,3,1]=>2479
[1,1,1,2,4]=>931
[1,1,1,3,1,1,1]=>3098
[1,1,1,3,1,2]=>2256
[1,1,1,3,2,1]=>2660
[1,1,1,3,3]=>1414
[1,1,1,4,1,1]=>1754
[1,1,1,4,2]=>1344
[1,1,1,5,1]=>704
[1,1,1,6]=>154
[1,1,2,1,1,1,1,1]=>4202
[1,1,2,1,1,1,2]=>2982
[1,1,2,1,1,2,1]=>3484
[1,1,2,1,1,3]=>1762
[1,1,2,1,2,1,1]=>3667
[1,1,2,1,2,2]=>2661
[1,1,2,1,3,1]=>2407
[1,1,2,1,4]=>901
[1,1,2,2,1,1,1]=>3754
[1,1,2,2,1,2]=>2694
[1,1,2,2,2,1]=>3164
[1,1,2,2,3]=>1634
[1,1,2,3,1,1]=>2704
[1,1,2,3,2]=>2019
[1,1,2,4,1]=>1399
[1,1,2,5]=>399
[1,1,3,1,1,1,1]=>3014
[1,1,3,1,1,2]=>2172
[1,1,3,1,2,1]=>2548
[1,1,3,1,3]=>1330
[1,1,3,2,1,1]=>2704
[1,1,3,2,2]=>1986
[1,1,3,3,1]=>1849
[1,1,3,4]=>721
[1,1,4,1,1,1]=>1754
[1,1,4,1,2]=>1304
[1,1,4,2,1]=>1540
[1,1,4,3]=>854
[1,1,5,1,1]=>794
[1,1,5,2]=>624
[1,1,6,1]=>254
[1,1,7]=>44
[1,2,1,1,1,1,1,1]=>4004
[1,2,1,1,1,1,2]=>2838
[1,2,1,1,1,2,1]=>3314
[1,2,1,1,1,3]=>1672
[1,2,1,1,2,1,1]=>3484
[1,2,1,1,2,2]=>2526
[1,2,1,1,3,1]=>2279
[1,2,1,1,4]=>851
[1,2,1,2,1,1,1]=>3556
[1,2,1,2,1,2]=>2550
[1,2,1,2,2,1]=>2994
[1,2,1,2,3]=>1544
[1,2,1,3,1,1]=>2548
[1,2,1,3,2]=>1902
[1,2,1,4,1]=>1315
[1,2,1,5]=>375
[1,2,2,1,1,1,1]=>3584
[1,2,2,1,1,2]=>2558
[1,2,2,1,2,1]=>2994
[1,2,2,1,3]=>1532
[1,2,2,2,1,1]=>3164
[1,2,2,2,2]=>2306
[1,2,2,3,1]=>2109
[1,2,2,4]=>801
[1,2,3,1,1,1]=>2660
[1,2,3,1,2]=>1942
[1,2,3,2,1]=>2290
[1,2,3,3]=>1224
[1,2,4,1,1]=>1540
[1,2,4,2]=>1182
[1,2,5,1]=>630
[1,2,6]=>140
[1,3,1,1,1,1,1]=>2717
[1,3,1,1,1,2]=>1947
[1,3,1,1,2,1]=>2279
[1,3,1,1,3]=>1177
[1,3,1,2,1,1]=>2407
[1,3,1,2,2]=>1761
[1,3,1,3,1]=>1622
[1,3,1,4]=>626
[1,3,2,1,1,1]=>2479
[1,3,2,1,2]=>1794
[1,3,2,2,1]=>2109
[1,3,2,3]=>1109
[1,3,3,1,1]=>1849
[1,3,3,2]=>1389
[1,3,4,1]=>994
[1,3,5]=>294
[1,4,1,1,1,1]=>1529
[1,4,1,1,2]=>1119
[1,4,1,2,1]=>1315
[1,4,1,3]=>709
[1,4,2,1,1]=>1399
[1,4,2,2]=>1041
[1,4,3,1]=>994
[1,4,4]=>406
[1,5,1,1,1]=>704
[1,5,1,2]=>534
[1,5,2,1]=>630
[1,5,3]=>364
[1,6,1,1]=>254
[1,6,2]=>204
[1,7,1]=>65
[1,8]=>9
[2,1,1,1,1,1,1,1]=>3432
[2,1,1,1,1,1,2]=>2431
[2,1,1,1,1,2,1]=>2838
[2,1,1,1,1,3]=>1430
[2,1,1,1,2,1,1]=>2982
[2,1,1,1,2,2]=>2161
[2,1,1,1,3,1]=>1947
[2,1,1,1,4]=>726
[2,1,1,2,1,1,1]=>3040
[2,1,1,2,1,2]=>2179
[2,1,1,2,2,1]=>2558
[2,1,1,2,3]=>1318
[2,1,1,3,1,1]=>2172
[2,1,1,3,2]=>1621
[2,1,1,4,1]=>1119
[2,1,1,5]=>319
[2,1,2,1,1,1,1]=>3054
[2,1,2,1,1,2]=>2179
[2,1,2,1,2,1]=>2550
[2,1,2,1,3]=>1304
[2,1,2,2,1,1]=>2694
[2,1,2,2,2]=>1963
[2,1,2,3,1]=>1794
[2,1,2,4]=>681
[2,1,3,1,1,1]=>2256
[2,1,3,1,2]=>1647
[2,1,3,2,1]=>1942
[2,1,3,3]=>1038
[2,1,4,1,1]=>1304
[2,1,4,2]=>1001
[2,1,5,1]=>534
[2,1,6]=>119
[2,2,1,1,1,1,1]=>3036
[2,2,1,1,1,2]=>2161
[2,2,1,1,2,1]=>2526
[2,2,1,1,3]=>1286
[2,2,1,2,1,1]=>2661
[2,2,1,2,2]=>1936
[2,2,1,3,1]=>1761
[2,2,1,4]=>666
[2,2,2,1,1,1]=>2728
[2,2,2,1,2]=>1963
[2,2,2,2,1]=>2306
[2,2,2,3]=>1198
[2,2,3,1,1]=>1986
[2,2,3,2]=>1486
[2,2,4,1]=>1041
[2,2,5]=>301
[2,3,1,1,1,1]=>2244
[2,3,1,1,2]=>1621
[2,3,1,2,1]=>1902
[2,3,1,3]=>998
[2,3,2,1,1]=>2019
[2,3,2,2]=>1486
[2,3,3,1]=>1389
[2,3,4]=>546
[2,4,1,1,1]=>1344
[2,4,1,2]=>1001
[2,4,2,1]=>1182
[2,4,3]=>658
[2,5,1,1]=>624
[2,5,2]=>491
[2,6,1]=>204
[2,7]=>36
[3,1,1,1,1,1,1]=>2002
[3,1,1,1,1,2]=>1430
[3,1,1,1,2,1]=>1672
[3,1,1,1,3]=>858
[3,1,1,2,1,1]=>1762
[3,1,1,2,2]=>1286
[3,1,1,3,1]=>1177
[3,1,1,4]=>451
[3,1,2,1,1,1]=>1806
[3,1,2,1,2]=>1304
[3,1,2,2,1]=>1532
[3,1,2,3]=>802
[3,1,3,1,1]=>1330
[3,1,3,2]=>998
[3,1,4,1]=>709
[3,1,5]=>209
[3,2,1,1,1,1]=>1834
[3,2,1,1,2]=>1318
[3,2,1,2,1]=>1544
[3,2,1,3]=>802
[3,2,2,1,1]=>1634
[3,2,2,2]=>1198
[3,2,3,1]=>1109
[3,2,4]=>431
[3,3,1,1,1]=>1414
[3,3,1,2]=>1038
[3,3,2,1]=>1224
[3,3,3]=>662
[3,4,1,1]=>854
[3,4,2]=>658
[3,5,1]=>364
[3,6]=>84
[4,1,1,1,1,1]=>1001
[4,1,1,1,2]=>726
[4,1,1,2,1]=>851
[4,1,1,3]=>451
[4,1,2,1,1]=>901
[4,1,2,2]=>666
[4,1,3,1]=>626
[4,1,4]=>251
[4,2,1,1,1]=>931
[4,2,1,2]=>681
[4,2,2,1]=>801
[4,2,3]=>431
[4,3,1,1]=>721
[4,3,2]=>546
[4,4,1]=>406
[4,5]=>126
[5,1,1,1,1]=>429
[5,1,1,2]=>319
[5,1,2,1]=>375
[5,1,3]=>209
[5,2,1,1]=>399
[5,2,2]=>301
[5,3,1]=>294
[5,4]=>126
[6,1,1,1]=>154
[6,1,2]=>119
[6,2,1]=>140
[6,3]=>84
[7,1,1]=>44
[7,2]=>36
[8,1]=>9
[9]=>1
                    

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 2\ q^{3} + q^{5}$

$F_{4} = q + 2\ q^{4} + q^{6} + 2\ q^{9} + q^{10} + q^{14}$

$F_{5} = q + 2\ q^{5} + 2\ q^{10} + 2\ q^{14} + q^{17} + q^{19} + 2\ q^{22} + 2\ q^{28} + 2\ q^{32} + q^{42}$

$F_{6} = q + 2\ q^{6} + 2\ q^{15} + 3\ q^{20} + q^{26} + 2\ q^{34} + 2\ q^{40} + 2\ q^{45} + 2\ q^{48} + q^{53} + 3\ q^{62} + 2\ q^{72} + 2\ q^{75} + q^{84} + 2\ q^{90} + 2\ q^{104} + q^{107} + q^{132}$

$F_{7} = q + 2\ q^{7} + 2\ q^{21} + 2\ q^{27} + 2\ q^{35} + q^{37} + 2\ q^{55} + 2\ q^{65} + q^{69} + 2\ q^{75} + 2\ q^{81} + 2\ q^{95} + 2\ q^{105} + 2\ q^{107} + 2\ q^{117} + q^{126} + 2\ q^{137} + 2\ q^{145} + 2\ q^{157} + 2\ q^{165} + 2\ q^{171} + 2\ q^{180} + 2\ q^{185} + q^{207} + 2\ q^{211} + 2\ q^{219} + q^{233} + 2\ q^{241} + 2\ q^{252} + 2\ q^{255} + q^{281} + 2\ q^{295} + 2\ q^{297} + 2\ q^{345} + 2\ q^{359} + q^{429}$

$F_{8} = q + 2\ q^{8} + 2\ q^{28} + 2\ q^{35} + q^{50} + 2\ q^{56} + q^{70} + 2\ q^{83} + 2\ q^{98} + 2\ q^{110} + 2\ q^{125} + 2\ q^{133} + 2\ q^{170} + 2\ q^{175} + 2\ q^{185} + 2\ q^{196} + 2\ q^{200} + q^{226} + 2\ q^{235} + q^{242} + 2\ q^{250} + q^{262} + 2\ q^{275} + 2\ q^{281} + 2\ q^{303} + 2\ q^{332} + 2\ q^{343} + 2\ q^{358} + 2\ q^{365} + 2\ q^{371} + 2\ q^{376} + 2\ q^{407} + 2\ q^{410} + 2\ q^{436} + q^{450} + 2\ q^{452} + q^{460} + 2\ q^{476} + 2\ q^{500} + 2\ q^{502} + 2\ q^{516} + 2\ q^{533} + 2\ q^{551} + q^{554} + 2\ q^{572} + 2\ q^{609} + 2\ q^{620} + 3\ q^{623} + 2\ q^{646} + 2\ q^{685} + q^{704} + 2\ q^{718} + 2\ q^{725} + 2\ q^{731} + 2\ q^{765} + 2\ q^{770} + 2\ q^{821} + 2\ q^{842} + q^{858} + 2\ q^{861} + 4\ q^{875} + q^{958} + 2\ q^{1001} + 2\ q^{1006} + 2\ q^{1026} + q^{1060} + 2\ q^{1166} + 2\ q^{1220} + q^{1234} + q^{1430}$

$F_{9} = q + 2\ q^{9} + 2\ q^{36} + 2\ q^{44} + q^{65} + 2\ q^{84} + 2\ q^{119} + 2\ q^{126} + 2\ q^{140} + 2\ q^{154} + 2\ q^{204} + 2\ q^{209} + q^{251} + 2\ q^{254} + 2\ q^{294} + 2\ q^{301} + 2\ q^{319} + 2\ q^{364} + 2\ q^{375} + 2\ q^{399} + 2\ q^{406} + 2\ q^{429} + 2\ q^{431} + 2\ q^{451} + q^{491} + 2\ q^{534} + 2\ q^{546} + 2\ q^{624} + 2\ q^{626} + 2\ q^{630} + 2\ q^{658} + q^{662} + 2\ q^{666} + 2\ q^{681} + 2\ q^{704} + 2\ q^{709} + 2\ q^{721} + 2\ q^{726} + q^{794} + 2\ q^{801} + 2\ q^{802} + 2\ q^{851} + 2\ q^{854} + q^{858} + 2\ q^{901} + 2\ q^{931} + 2\ q^{994} + 2\ q^{998} + 4\ q^{1001} + 2\ q^{1038} + 2\ q^{1041} + 2\ q^{1109} + 2\ q^{1119} + 2\ q^{1177} + 2\ q^{1182} + 2\ q^{1198} + 2\ q^{1224} + 2\ q^{1286} + 4\ q^{1304} + 2\ q^{1315} + 2\ q^{1318} + 2\ q^{1330} + 2\ q^{1344} + 2\ q^{1389} + 2\ q^{1399} + 2\ q^{1414} + 2\ q^{1430} + 2\ q^{1486} + 2\ q^{1529} + 2\ q^{1532} + 2\ q^{1540} + 2\ q^{1544} + 2\ q^{1621} + q^{1622} + 2\ q^{1634} + q^{1647} + 2\ q^{1672} + 2\ q^{1754} + 2\ q^{1761} + 2\ q^{1762} + 2\ q^{1794} + 2\ q^{1806} + 2\ q^{1834} + 2\ q^{1849} + 2\ q^{1902} + q^{1936} + 2\ q^{1942} + 2\ q^{1947} + 2\ q^{1963} + 2\ q^{1986} + 2\ q^{2002} + 2\ q^{2019} + 2\ q^{2109} + 2\ q^{2161} + 2\ q^{2172} + 2\ q^{2179} + 2\ q^{2244} + 2\ q^{2256} + 2\ q^{2279} + q^{2290} + 2\ q^{2306} + 2\ q^{2407} + q^{2431} + 2\ q^{2479} + 2\ q^{2526} + 2\ q^{2548} + 2\ q^{2550} + 2\ q^{2558} + 2\ q^{2660} + 2\ q^{2661} + 2\ q^{2694} + 2\ q^{2704} + 2\ q^{2717} + 2\ q^{2728} + 2\ q^{2838} + 2\ q^{2982} + 2\ q^{2994} + 2\ q^{3014} + 2\ q^{3036} + 2\ q^{3040} + 2\ q^{3054} + q^{3098} + 2\ q^{3164} + q^{3314} + 2\ q^{3432} + 2\ q^{3484} + 2\ q^{3556} + 2\ q^{3584} + q^{3667} + 2\ q^{3754} + 2\ q^{4004} + 2\ q^{4202} + 2\ q^{4274} + q^{4862}$

Description

Number of parabolic noncrossing partitions indexed by the composition.
Also the number of elements in the $\nu$-Tamari lattice with $\nu = \nu_\alpha = 1^{\alpha_1} 0^{\alpha_1} \cdots 1^{\alpha_k} 0^{\alpha_k}$, the bounce path indexed by the composition $\alpha$. These elements are Dyck paths weakly above the bounce path $\nu_\alpha$.

References

[1] Mühle, H., Williams, N. Tamari Lattices for Parabolic Quotients of the Symmetric Group arXiv:1804.02761
[2] Bergeron, N., Ceballos, C., Pilaud, V. Hopf dreams arXiv:1807.03044

Code

def contains(A,B):
    Aa = A.to_area_sequence()
    Bb = B.to_area_sequence()
    return all( Aa[i] >= Bb[i] for i in range(len(Aa)) )

def statistic(L):
    n = sum(list(L))
    Bp = []
    for a in L:
        Bp += ([1] * a) + ([0] * a)
    Bp = DyckWord(Bp)
    return sum(1 for D in DyckWords(n) if contains(D, Bp))

Created

Dec 12, 2018 at 11:36 by Wenjie Fang

Updated

Dec 13, 2018 at 19:02 by Martin Rubey