Finite non-cancellative commutative monoids

Up:Monoid enumeration
139 unique, 2403 total

Σ#PresentationPropertiesDescriptionφ
657⟨a, b | aa=a, bb=a⟩Noc Com 4ℕ(4 = 2)37
659⟨a, b | aa=b, ab=a⟩Noc Com 3ℕ(3 = 1)61
660⟨a, b | aa=b, ab=b⟩Noc Com 3ℕ(3 = 2)23
661⟨a, b | aa=b, bb=a⟩Noc Com 4ℕ(4 = 1)72
7159⟨a, b | ab=aa, bb=a⟩Noc Com 4ℕ(4 = 3)16
7236⟨a, b | aa=a, aaa=b⟩Noc Com 2ℕ(2 = 1)46
7245⟨a, b | aa=a, bbb=a⟩Noc Com 6ℕ(6 = 3)49
7253⟨a, b | aa=b, abb=a⟩Noc Com 5ℕ(5 = 1)71
7254⟨a, b | aa=b, abb=b⟩Noc Com 5ℕ(5 = 2)43
7257⟨a, b | aa=b, bbb=a⟩Noc Com 6ℕ(6 = 1)61
7258⟨a, b | aa=b, bbb=b⟩Noc Com 6ℕ(6 = 2)55
7280⟨a, b | ab=a, bb=aa⟩Noc Com 417
8571⟨a, b | aaa=a, bbb=a⟩Noc Com 9ℕ(9 = 3)48
8574⟨a, b | aaa=b, aab=b⟩Noc Com 5ℕ(5 = 3)27
8577⟨a, b | aaa=b, abb=a⟩Noc Com 7ℕ(7 = 1)59
8578⟨a, b | aaa=b, abb=b⟩Noc Com 7ℕ(7 = 3)44
8581⟨a, b | aaa=b, bbb=a⟩Noc Com 9ℕ(9 = 1)62
8644⟨a, b | ab=aa, bbb=a⟩Noc Com 6ℕ(6 = 4)46
8891⟨a, b | aa=a, abba=b⟩Noc Com 312
8898⟨a, b | aa=a, bbbb=a⟩Noc Com 8ℕ(8 = 4)48
8913⟨a, b | aa=b, abbb=b⟩Noc Com 7ℕ(7 = 2)82
8918⟨a, b | aa=b, bbbb=a⟩Noc Com 8ℕ(8 = 1)34
8919⟨a, b | aa=b, bbbb=b⟩Noc Com 8ℕ(8 = 2)46
8950⟨a, b | ab=a, bbbb=a⟩Noc Com 5ℕ(5 = 4)32
8995⟨a, b | ab=a, aaa=bb⟩Noc Com 519
81020⟨a, b | ab=a, bbb=aa⟩Noc Com 59
91584⟨a, b | aaa=aa, bbb=a⟩Noc Com 9ℕ(9 = 6)16
91598⟨a, b | aaa=ab, bbb=a⟩Noc Com 9ℕ(9 = 4)40
91601⟨a, b | aaa=bb, aab=b⟩Noc Com 75
91605⟨a, b | aaa=bb, abb=b⟩Noc Com 8ℕ(8 = 3)55
91606⟨a, b | aaa=bb, bab=a⟩Noc Com 814
91608⟨a, b | aaa=bb, bbb=a⟩Noc Com 9ℕ(9 = 2)70
91620⟨a, b | aab=aa, bbb=a⟩Noc Com 7ℕ(7 = 6)35
91632⟨a, b | aab=ab, bbb=a⟩Noc Com 7ℕ(7 = 4)50
91648⟨a, b | aab=bb, abb=a⟩Noc Com 613
91686⟨a, b | abb=aa, bbb=a⟩Noc Com 6ℕ(6 = 5)49
91998⟨a, b | aaa=a, bbbb=a⟩Noc Com 12ℕ(12 = 4)6
92012⟨a, b | aaa=b, abbb=a⟩Noc Com 10ℕ(10 = 1)59
92013⟨a, b | aaa=b, abbb=b⟩Noc Com 10ℕ(10 = 3)35
92018⟨a, b | aaa=b, bbbb=a⟩Noc Com 12ℕ(12 = 1)27
92019⟨a, b | aaa=b, bbbb=b⟩Noc Com 12ℕ(12 = 3)23
92074⟨a, b | aab=b, babb=a⟩Noc Com 720
92206⟨a, b | ab=aa, bbbb=a⟩Noc Com 8ℕ(8 = 5)32
92220⟨a, b | bb=aa, aaab=a⟩Noc Com 822
92881⟨a, b | aa=a, abbba=b⟩Noc Com 48
92894⟨a, b | aa=a, bbbbb=a⟩Noc Com 10ℕ(10 = 5)17
92935⟨a, b | aa=b, bbbbb=b⟩Noc Com 10ℕ(10 = 2)57
93075⟨a, b | ab=a, aaaa=bb⟩Noc Com 614
93132⟨a, b | ab=a, bbbb=aa⟩Noc Com 65
93193⟨a, b | ab=a, bbb=aaa⟩Noc Com 69
104130⟨a, b | aab=aaa, bbb=a⟩Noc Com 9ℕ(9 = 7)1
104156⟨a, b | abb=aaa, bbb=a⟩Noc Com 9ℕ(9 = 5)12
104162⟨a, b | abb=aab, bbb=a⟩Noc Com 7ℕ(7 = 5)42
104630⟨a, b | aaaa=a, bbbb=a⟩Noc Com 16ℕ(16 = 4)1
104637⟨a, b | aaaa=b, aabb=b⟩Noc Com 10ℕ(10 = 4)20
104642⟨a, b | aaaa=b, abbb=a⟩Noc Com 13ℕ(13 = 1)10
104643⟨a, b | aaaa=b, abbb=b⟩Noc Com 13ℕ(13 = 4)6
104648⟨a, b | aaaa=b, bbbb=a⟩Noc Com 16ℕ(16 = 1)5
105033⟨a, b | aaa=aa, abba=b⟩Noc Com 42
105040⟨a, b | aaa=aa, bbbb=a⟩Noc Com 12ℕ(12 = 8)
105072⟨a, b | aaa=ab, bbbb=a⟩Noc Com 12ℕ(12 = 5)7
105079⟨a, b | aaa=bb, aaba=b⟩Noc Com 98
105086⟨a, b | aaa=bb, abbb=a⟩Noc Com 1111
105087⟨a, b | aaa=bb, abbb=b⟩Noc Com 113
105092⟨a, b | aaa=bb, bbbb=a⟩Noc Com 12ℕ(12 = 2)43
105124⟨a, b | aab=aa, bbbb=a⟩Noc Com 9ℕ(9 = 8)5
105191⟨a, b | aab=bb, aaaa=b⟩Noc Com 8ℕ(8 = 6)18
106276⟨a, b | aaa=a, bbbbb=a⟩Noc Com 15ℕ(15 = 5)
106292⟨a, b | aaa=b, aabbb=a⟩Noc Com 11ℕ(11 = 1)35
106293⟨a, b | aaa=b, aabbb=b⟩Noc Com 11ℕ(11 = 3)11
106305⟨a, b | aaa=b, abbbb=b⟩Noc Com 13ℕ(13 = 3)2
106316⟨a, b | aaa=b, bbbbb=a⟩Noc Com 15ℕ(15 = 1)
106317⟨a, b | aaa=b, bbbbb=b⟩Noc Com 15ℕ(15 = 3)
106380⟨a, b | aab=a, bbbbb=a⟩Noc Com 11ℕ(11 = 5)1
106587⟨a, b | aaa=b, abbb=bb⟩Noc Com 10ℕ(10 = 6)3
106597⟨a, b | aaa=b, bbbb=bb⟩Noc Com 12ℕ(12 = 6)4
106824⟨a, b | aab=b, bbb=aaa⟩Noc Com 95
108617⟨a, b | aa=a, abbbba=b⟩Noc Com 53
108691⟨a, b | aa=b, abbbbb=b⟩Noc Com 11ℕ(11 = 2)32
108987⟨a, b | ab=a, aaaaa=bb⟩Noc Com 75
109108⟨a, b | ab=a, bbbbb=aa⟩Noc Com 72
109263⟨a, b | ab=a, aaaa=bbb⟩Noc Com 74
109376⟨a, b | ab=a, bbbb=aaa⟩Noc Com 73
1112164⟨a, b | aaaa=aa, bbbb=a⟩Noc Com 16ℕ(16 = 8)
1112179⟨a, b | aaaa=ab, abbb=b⟩Noc Com 11ℕ(11 = 4)20
1112194⟨a, b | aaaa=ab, bbbb=a⟩Noc Com 16ℕ(16 = 5)2
1112196⟨a, b | aaaa=bb, aaab=a⟩Noc Com 107
1112197⟨a, b | aaaa=bb, aaab=b⟩Noc Com 101
1112206⟨a, b | aaaa=bb, abbb=a⟩Noc Com 141
1112207⟨a, b | aaaa=bb, abbb=b⟩Noc Com 141
1112212⟨a, b | aaaa=bb, bbbb=a⟩Noc Com 16ℕ(16 = 2)
1112240⟨a, b | aaab=aa, bbbb=a⟩Noc Com 13ℕ(13 = 8)1
1112268⟨a, b | aaab=ab, bbbb=a⟩Noc Com 13ℕ(13 = 5)3
1112324⟨a, b | aaab=bb, bbbb=a⟩Noc Com 13ℕ(13 = 2)14
1112452⟨a, b | aabb=aa, bbbb=a⟩Noc Com 10ℕ(10 = 8)3
1112606⟨a, b | abbb=aa, bbbb=a⟩Noc Com 8ℕ(8 = 7)14
1112910⟨a, b | aab=aaa, bbbb=a⟩Noc Com 12ℕ(12 = 9)2
1114367⟨a, b | aaaa=a, bbbbb=a⟩Noc Com 20ℕ(20 = 5)
1114383⟨a, b | aaaa=b, aabbb=a⟩Noc Com 14ℕ(14 = 1)15
1114384⟨a, b | aaaa=b, aabbb=b⟩Noc Com 14ℕ(14 = 4)5
1114395⟨a, b | aaaa=b, abbbb=a⟩Noc Com 17ℕ(17 = 1)2
1114396⟨a, b | aaaa=b, abbbb=b⟩Noc Com 17ℕ(17 = 4)2
1114407⟨a, b | aaaa=b, bbbbb=a⟩Noc Com 20ℕ(20 = 1)
1114408⟨a, b | aaaa=b, bbbbb=b⟩Noc Com 20ℕ(20 = 4)
1114647⟨a, b | aaba=b, babbb=a⟩Noc Com 132
1115426⟨a, b | aaa=aa, abbba=b⟩Noc Com 5
1115439⟨a, b | aaa=aa, bbbbb=a⟩Noc Com 15ℕ(15 = 10)
1115503⟨a, b | aaa=ab, bbbbb=a⟩Noc Com 15ℕ(15 = 6)1
1115520⟨a, b | aaa=bb, aabbb=b⟩Noc Com 132
1115532⟨a, b | aaa=bb, abbbb=b⟩Noc Com 14ℕ(14 = 3)11
1115539⟨a, b | aaa=bb, babbb=a⟩Noc Com 14
1115543⟨a, b | aaa=bb, bbbbb=a⟩Noc Com 15ℕ(15 = 2)1
1115607⟨a, b | aab=aa, bbbbb=a⟩Noc Com 11ℕ(11 = 10)1
1115671⟨a, b | aab=ab, bbbbb=a⟩Noc Com 11ℕ(11 = 6)8
1115738⟨a, b | aab=bb, aaaaa=b⟩Noc Com 10ℕ(10 = 7)7
1118758⟨a, b | aaa=a, bbbbbb=a⟩Noc Com 18ℕ(18 = 6)
1118811⟨a, b | aaa=b, abbbbb=b⟩Noc Com 16ℕ(16 = 3)2
1118830⟨a, b | aaa=b, bbbbbb=a⟩Noc Com 18ℕ(18 = 1)
1118831⟨a, b | aaa=b, bbbbbb=b⟩Noc Com 18ℕ(18 = 3)
1118958⟨a, b | aab=a, bbbbbb=a⟩Noc Com 13ℕ(13 = 6)4
1119070⟨a, b | aab=b, bbabbb=a⟩Noc Com 114
1119374⟨a, b | aaa=b, bbbbb=ab⟩Noc Com 15ℕ(15 = 4)
1119507⟨a, b | aab=b, aaaaa=bb⟩Noc Com 9
1119564⟨a, b | aab=b, abbbb=aa⟩Noc Com 105
1119773⟨a, b | aba=b, bbbbb=aa⟩Noc Com 12
1119899⟨a, b | aaa=b, abbb=bbb⟩Noc Com 10ℕ(10 = 9)1
1119917⟨a, b | aaa=b, bbbb=abb⟩Noc Com 12ℕ(12 = 7)2
1120051⟨a, b | aab=b, aaaa=abb⟩Noc Com 81
1120168⟨a, b | aab=b, bbbb=aaa⟩Noc Com 11
1120253⟨a, b | aba=b, aaaa=bbb⟩Noc Com 10
1120686⟨a, b | bb=aa, aaaaab=a⟩Noc Com 1215
1124145⟨a, b | aa=a, abbbbba=b⟩Noc Com 6
1124186⟨a, b | aa=a, bbbbbbb=a⟩Noc Com 14ℕ(14 = 7)
1124331⟨a, b | aa=b, bbbbbbb=b⟩Noc Com 14ℕ(14 = 2)
1124863⟨a, b | ab=a, aaaaaa=bb⟩Noc Com 8
1125112⟨a, b | ab=a, bbbbbb=aa⟩Noc Com 8
1125411⟨a, b | ab=a, aaaaa=bbb⟩Noc Com 8
1125652⟨a, b | ab=a, bbbbb=aaa⟩Noc Com 8
1125897⟨a, b | ab=a, bbbb=aaaa⟩Noc Com 8