There are 125 operads in the database.
This is just a big table, used more for testing purposes. This is not the layout I intend for the final product.
| name | abbreviations | dimension | OEIS | dimension formula | series | category | properties | Koszul dual |
|---|---|---|---|---|---|---|---|---|
| Associative | As, Ass, Assoc | 1, 1, 1, 1, 1, 1, 1, 1, 1 | OEIS: A000012 | 1 | x / (1 - x) | set | Koszul, binary, quadratic, cyclic, Hopf | As |
| Lie | Lie | 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 | OEIS: A000142 | factorial(n - 1) | -log(1 - x) | vec | Koszul, binary, quadratic, cyclic, NielsenSchreier | Com |
| Pre-Lie | PreLie | 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000 | OEIS: A000169 | n**(n - 1) | (x * exp(-x)).reverse() | vec | Koszul, binary, quadratic, anticyclic, NielsenSchreier | Perm |
| F-Manifold | FMan | 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000 | OEIS: A000169 | n**(n - 1) | (x * exp(-x)).reverse() | Zvec | binary | |
| DoubleLie | DoubleLie, Lie2 | 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000 | OEIS: A000169 | n**(n - 1) | (x * exp(-x)).reverse() | vec | Koszul, binary, quadratic | Com2 |
| Non-Associative Permutative | NAP | 1, 2, 9, 64, 625, 7776, 117649, 2097152, 43046721, 1000000000 | OEIS: A000169 | n**(n - 1) | (x*exp(-x)).reverse() | set | Koszul, binary, quadratic | NAP! |
| Permutative | Perm | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | OEIS: A000027 | n | x*exp(x) | set | Koszul, binary, quadratic, anticyclic | PreLie |
| DoubleCommutative | Com2 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | OEIS: A000027 | n | x*exp(x) | vec | Koszul, binary, quadratic | DoubleLie |
| NAP! | NAP! | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | OEIS: A000027 | n | x*exp(x) | vec | Koszul, binary, quadratic | NAP |
| Commutative | Com, Comm | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 | OEIS: A000012 | 1 | exp(x) - 1 | set | Koszul, binary, quadratic, Hopf, cyclic | Lie |
| Leibniz | Leib | 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 | OEIS: A000142 | factorial(n) | x/(1-x) | vec | Koszul, binary, quadratic, anticyclic | Zin |
| Zinbiel | Zin, Zinb | 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 | OEIS: A000142 | factorial(n) | x/(1-x) | vec | Koszul, binary, quadratic, anticyclic | Leib |
| Dendriforme | Dend | 1, 2, 5, 14, 42, 132, 429, 1430, 4862 | OEIS: A000108 | binomial(2*n,n)/(n+1) | (x/(1+x)**2).reverse() | vec | Koszul, binary, quadratic, anticyclic | Dias |
| Diassociative | Dias | 1, 2, 3, 4, 5, 6, 7, 8, 9 | OEIS: A000027 | n | x/(1-x)**2 | set | Koszul, binary, quadratic, anticyclic | Dend |
| Poisson | Pois, Poiss | 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 | OEIS: A000142 | factorial(n) | x/(1-x) | Zvec | Koszul, binary, quadratic, cyclic | Pois |
| Gerstenhaber | Gerst | 1, 1-t, 2*t^2 - 3*t + 1, -6*t^3 + 11*t^2 - 6*t + 1 | prod(1 - k*t for k in range(1,n)) | dgvec | Koszul, binary, quadratic, Hopf | Gerst | ||
| Lambda | Ī | 1, 2-t, 2*t^2 - 9*t + 9, -6*t^3 + 44*t^2 - 96*t + 64 | prod(n - k*t for k in range(1, n)) | dgvec | binary, quadratic | Pasc | ||
| Pascal | Pasc | 1, 2-t, 3-3*t+t^2, 4-6*t+4*t^2-t^3 | (exp(x)-exp((1-t)*x))/t | dgvec | Ī | |||
| Triassociative | Trias | 1, 3, 7, 15, 31, 63, 127, 255, 511 | OEIS: A000225 | 2**n-1 | x/(1-x)/(1-2*x) | set | binary, quadratic, Koszul | Tridend |
| Tridendriforme | Tridend | 1, 3, 11, 45, 197 | OEIS: A001003 | -(-1+3*x+sqrt(1-6*x+x**2))/(4*x) | Zvec | binary, quadratic, Koszul | Trias | |
| K | K | 1, 2-t, 5-5*t+t**2, 14-21*t+9*t**2-t**3 | dgvec | binary, quadratic, Koszul | ||||
| Diptere | Dipt | 1, 2, 6, 22, 90, 394, 1806 | OEIS: A006318 | (1-x-sqrt(1-6*x+x**2))/2 | set | Koszul, binary, quadratic | Dipt! | |
| Dual Diptere | Dipt! | 1, 2, 2, 2, 2, 2 | OEIS: A040000 | lambda n: 1 if n <= 1 else 2 | (x+x**2)/(1-x) | vec | Koszul, binary, quadratic | Dipt |
| 2-associative | 2as | 1, 2, 6, 22, 90, 394, 1806 | OEIS: A006318 | (1-x-sqrt(1-6*x+x**2))/2 | Zset | Koszul, binary, quadratic, cyclic | 2as! | |
| Dual 2-associative | 2as! | 1, 2, 2, 2, 2, 2, 2 | OEIS: A040000 | lambda n: 1 if n <= 1 else 2 | (x+x**2)/(1-x) | Zvec | Koszul, binary, quadratic, cyclic | 2as |
| 3-associative | 3as | 1, 3, 15, 93, 645, 4791, 37275, 299865 | OEIS: A103210 | set | Koszul, binary, quadratic | |||
| Arbustive | Arb | 1, 3, 19, 195, 2791, 51303, 1152019, 30564075 | OEIS: A048172 | (log(1+x)-x**2/(1+x)).reverse() | set | binary, quadratic, Koszul | ||
| WithoutNPosets | WNP | 1, 3, 19, 195, 2791, 51303, 1152019, 30564075 | OEIS: A048172 | (log(1+x)-x**2/(1+x)).reverse() | set | binary, quadratic, Koszul | ||
| NablaCompatiblePosets | CPā | 1, 3, 19, 195, 2791, 51303, 1152019, 30564075 | OEIS: A048172 | (log(1+x)-x**2/(1+x)).reverse() | set | binary, quadratic, Koszul | ||
| Post-Lie | PostLie | 1, 3, 20, 210, 3024, 55440 | OEIS: A006963 | lambda n: 1 if n == 1 else factorial(2*n-1)/factorial(n) | -log((1+sqrt(1-4*x))/2) | vec | Koszul, binary, quadratic | ComTrias |
| Commutative-Triassociative | ComTrias | 1, 3, 7, 15, 31, 63, 127 | OEIS: A000225 | 2**n-1 | (log((1+sqrt(1+4*x))/2)).reverse() | vec | binary, quadratic, Koszul | PostLie |
| Commutative-Tridendriform | CTD, Pi | 1, 3, 13, 75, 541, 4683 | OEIS: A000670 | (exp(x) - 1) / (2 - exp(x)) | vec | binary, quadratic, Koszul | CTD! | |
| Dual Commutative-Tridendriform | CTD! | 1, 3, 14, 90, 744 | OEIS: A029767 | factorial(n - 1) * (2**n - 1) | (-(exp(-x) - 1) / (2 - exp(-x))).reverse() | vec | binary, quadratic, Koszul | CTD |
| L-Dendriform | L-dend | 1, 4, 36, 480 | vec | binary, quadratic, non-Koszul | ||||
| Ennea | Ennea | 1, 9, 113 | vec | |||||
| Batalin-Vilkovisky | BV | 1-t, (1-t)**3, (1-t)**4*(1-2*t) | dgvec | cyclic | ||||
| Magmatic | Mag, PRT | 1, 1, 2, 5, 14, 42 | OEIS: A000108 | binomial(2*n-2,n-1)/n | (1-sqrt(1-4*x))/2 | set | binary, quadratic, Koszul, free, cyclic, NielsenSchreier | Nil2 |
| 2-nilpotent | Nil2 | 1, 1, 0, 0, 0, 0 | x + x**2 | vec | binary, quadratic, Koszul, monomial, cyclic | Mag | ||
| Commutative-Magmatic | ComMag, Griess | 1, 1, 3, 15, 105 | OEIS: A001147 | ZZ(2*n-3).multifactorial(2) | 1 - sqrt(1-2*x) | set | binary, quadratic, Koszul, free | ComMag! |
| Antisymmetric-Nilpotent | ComMag!, SkewNil2 | 1, 1, 0, 0, 0 | lambda n: 1 if n <= 2 else 0 | x + x**2/2 | vec | binary, quadratic, Koszul, monomial | ComMag | |
| Antisymmetric-Magmatic | SkewMag | 1, 1, 3, 15, 105 | OEIS: A001147 | ZZ(2*n-3).multifactorial(2) | 1 - sqrt(1-2*x) | vec | binary, quadratic, Koszul, free | SkewMag! |
| Commutative-Nilpotent | SkewMag!, ComNil2 | 1, 1, 0, 0, 0 | lambda n: 1 if n <= 2 else 0 | x + x**2/2 | vec | binary, quadratic, Koszul, monomial | SkewMag | |
| Quadri-algebra | Quad | 1, 4, 23, 156, 1162 | OEIS: A007297 | sum(binomial(3*n,n+1+j)*binomial(j-1,j-n) for j in range(n,2*n))/n | (x*(1-x)/(1+x)**3).reverse() | vec | binary, quadratic, Koszul, cyclic | Quad! |
| Dual Quadri-algebra | Quad! | 1, 4, 9, 16, 25 | OEIS: A000290 | n**2 | x*(1+x)/(1-x)**3 | vec | binary, quadratic, Koszul, cyclic | Quad |
| Noncrossing-Plants | NCP | 1, 3, 14, 80, 510, 3479, 24848, 183465 | OEIS: A121873 | (x*(1-x-x**2)/(1+x)**2).reverse() | set | binary, quadratic, Koszul | ||
| Triplicial | Trip | 1, 3, 12, 55, 273, 1428 | OEIS: A001764 | binomial(3*n,n)/(2*n+1) | set | binary, quadratic, Koszul | ||
| Bigraft | Bigraft | 1, 3, 12, 55, 273, 1428 | OEIS: A001764 | binomial(3*n,n)/(2*n+1) | set | binary, quadratic, Koszul | ||
| Triduplicial | TriDup | 1, 3, 11, 45, 197, 903, 4279 | OEIS: A001003 | -(-1+3*x+sqrt(1-6*x+x**2))/(4*x) | set | binary, quadratic, Koszul | TriDup! | |
| Dual Triduplicial | TriDup! | 1, 3, 7, 15, 31, 63, 127 | OEIS: A000225 | 2**n-1 | 1/(1-2*x)-1/(1-x) | vec | binary, quadratic, Koszul | TriDup |
| Terpliciale | Terp | 1, 3, 11, 45, 197, 903, 4279 | OEIS: A001003 | -(-1+3*x+sqrt(1-6*x+x**2))/(4*x) | set | binary, quadratic, Koszul | ||
| Duplicial | Dup | 1, 2, 5, 14, 42, 132, 429, 1430, 4862 | OEIS: A000108 | binomial(2*n,n)/(n+1) | (x/(1+x)**2).reverse() | set | Koszul, binary, quadratic | Dup! |
| Dual Duplicial | Dup! | 1, 2, 3, 4, 5, 6 | OEIS: A000027 | n | x/(1-x)**2 | vec | Koszul, binary, quadratic | Dup |
| Skew Duplicial | SkewDup | 1, 2, 5, 14, 42, 132, 429, 1430, 4862 | OEIS: A000108 | binomial(2*n,n)/(n+1) | (x/(1+x)**2).reverse() | set | binary, quadratic, Koszul | SkewDup! |
| Dual Skew Duplicial | SkewDup! | 1, 2, 3, 4, 5, 6 | OEIS: A000027 | n | x/(1-x)**2 | vec | binary, quadratic, Koszul | SkewDup |
| Alternative | Alt, Altern | 1, 2, 7, 32, 175, 1080 | OEIS: A161392 | vec | binary, quadratic, non-Koszul | |||
| Left-Alternative | LeftAlt, LAlt | 1, 2, 9, 60, 530, 5820 | OEIS: A161391 | vec | binary, quadratic, non-Koszul | |||
| Magmatic-Fine | MagFine | 1, 0, 1, 2, 6, 18, 57, 186, 622, 2120, 7338 | OEIS: A000957 | (1+2*x-sqrt(1-4*x))/(2*(2+x)) | vec | quadratic, Koszul, free | MagFine! | |
| Dual Magmatic-Fine | MagFine! | 1, 0, 1, 2, 3, 4 | x + x**3/(1-x)**2 | vec | quadratic, Koszul | MagFine | ||
| Brace | Brace | 1, 2, 12, 120, 1680, 30240, 665280 | OEIS: A001813 | binomial(2*n-2,n-1)/(n)*factorial(n) | (1-sqrt(1-4*x))/2 | vec | ||
| Moufang | Moufang | 1, 2, 7, 40 | vec | binary, cubic | ||||
| Malcev | Malcev | 1, 1, 3, 10, 44, 210, 1112, 6636 | vec | |||||
| Novikov | Novikov | 1, 2, 6, 20, 70, 252, 924 | OEIS: A000984 | binomial(2*n-2,n-1) | vec | binary, quadratic, non-Koszul | ||
| Akivis | Akivis | 1, 1, 8 | vec | free | ||||
| Sabinin | Sabinin | 1, 1, 8, 78, 1104 | log(1+(1-sqrt(1-4*x))/2) | vec | free | |||
| Jordan triple | JordanTriple | 1, 0, 3, 0, 55, 0 | vec | quadratic, ternary | ||||
| Jordan | Jordan | 1, 1, 3, 11, 55, 330, 2345, 19089 | OEIS: A001776 | vec | quadratic, cyclic | |||
| Totally-Associative Ternary | tAs-3 | 1, 0, 1, 0, 1, 0, 1 | OEIS: A000035 | x/(1-x**2) | set | ternary, quadratic | ||
| semi-Heap | semiHeap | 1, 0, 6, 0, 120 | set | ternary, quadratic | ||||
| Partially-Associative Ternary | pAs-3 | 1, 0, 1, 0, 2, 0, 5, 0, 14 | OEIS: A126120 | vec | ternary, quadratic | |||
| Lie Triple | LTS, LieTriple | 1, 0, 2, 0, 24, 0, 720 | OEIS: A005359 | lambda n: factorial(n-1) if n % 2 == 1 else 0 | vec | ternary, quadratic, Koszul | ||
| Lie-Yamaguti | LieYamaguti, LY | 1, 1, 5 | vec | |||||
| Interchange | Interchange | 1, 4 | set | binary, cubic | ||||
| Level | level | 1, 1, 3, 13, 75, 525, 4347, 41245, 441675 | OEIS: A007178 | set | binary, cubic | |||
| Hypercommutative | HyperCom, HyperComm | 1, 1, 1+t**2, 1+5*t**2+t**4, 1+16*t**2+16*t**4+t**6, 1+42*t**2+127*t**4+42*t**6+t**8, 1+99*t**2+715*t**4+715*t**6+99*t**8+t**10 | OEIS: A074060 | dgvec | quadratic, Koszul | Gravity | ||
| 2-Gerstenhaber | 2-Gerst | 1, 1, -t + 1, -4*t + 1, 9*t^2 - 10*t + 1, 64*t^2 - 20*t + 1 | prod(1-(n-2-k)**2 * t for k in range(0,n-2,2)) | dgvec | quadratic | |||
| Gravity | Gravity | 1, 1, - 2*t + 1, 6*t^2 - 5*t + 1, -24*t^3 + 26*t^2 - 9*t + 1 | prod(1 - k*t for k in range(2, n)) | dgvec | quadratic, Koszul | HyperCom | ||
| Alia | Alia | 1, 2, 11, 100, 1270, 20720, 413000 | OEIS: A220433 | (x-x**2+x**3/6).reverse() | vec | binary, quadratic, Koszul, NielsenSchreier | Alia! | |
| Lie-admissible | LieAdm | 1, 2, 11, 101, 1299, 21484, 434314 | OEIS: A337017 | (1-(-x).exp()-x**2/2).reverse() | vec | binary, quadratic, Koszul | LieAdm! | |
| Third-Power-Associative | 3PowAss | 1, 2, 11, 100, 1270, 20720, 413000 | OEIS: A220433 | (x-x**2+x**3/6).reverse() | vec | binary, quadratic | ||
| V | V | 1, 0, -t, 0, 2*t**2, 0, -5*t**3, 0, 14*t**4 | dgvec | ternary, quadratic, anticyclic, Koszul | ||||
| Hochschild | Hoch | 1, 2, 6, 22, 90, 394, 1806 | OEIS: A006318 | (1-x-sqrt(1-6*x+x**2))/2 | vec | binary, quadratic, Koszul, cyclic | Hoch! | |
| Dual Hochschild | Hoch! | 1, 2, 2, 2, 2, 2, 2 | OEIS: A040000 | lambda n: 1 if n <= 1 else 2 | (x+x**2)/(1-x) | vec | binary, quadratic, Koszul, cyclic | Hoch |
| Left-Nilpotent | LeftNil | 1, 1, 1, 1, 1, 1 | OEIS: A000012 | 1 | x/(1-x) | vec | Koszul, binary, quadratic, monomial | LeftNil |
| RW | FF4, GR4, RW | 1, 4, 24, 176, 1440, 12608 | OEIS: A156017 | -1/2*x - 1/4*sqrt(4*x**2 - 12*x + 1) + 1/4 | set | binary, quadratic, Koszul | ||
| RWT | RWT | 1, 3, 13, 68, 395, 2450, 15892, 106489 | OEIS: A200757 | set | binary, quadratic, Koszul | |||
| RWT-Sigma | RWT-Sigma | 1, 3, 16, 133, 1521, 22184 | OEIS: A048802 | set | binary | |||
| Noncrossing Trees | NCT, RWD | 1, 2, 7, 30, 143, 728, 3876, 21318 | OEIS: A006013 | binomial(3*n-2,n-1)/n | (x*(1-x)**2).reverse() | Zset | binary, quadratic, Koszul | |
| Hybridative | Hyb | 1, 2, 7, 31, 154, 820, 4575, 26398 | OEIS: A007863 | sum(binomial(n+k-1,k)*binomial(n+k,n-1-k) for k in range(n))/n | Zset | binary, quadratic, cyclic, Koszul | ||
| Bicolored Noncrossing Configurations | BNC | 1, 8, 80, 992, 13760, 204416 | OEIS: A234596 | 1/6*(1-4*x-(1-20*x+4*x^2).sqrt()) | set | binary, quadratic, Koszul | ||
| FF6 | FF6 | 1, 6, 56, 640, 8158, 111258, 1588544, 23446248 | OEIS: A231690 | (x*(1-3*x-x**2+x**3)/(1+3*x+x**2-x**3)).reverse() | set | binary, quadratic, Koszul | ||
| noncommutative HyperCom | ncHyperCom | 1, 1, 2, 5, 14, 42, 132 | OEIS: A000108 | binomial(2*n-2, n-1)/n | dgvec | quadratic, Koszul | ncGrav | |
| noncommutative Gerstenhaber | ncGerst | 1, 1 - t, 1-2*t+t**2 | dgvec | binary, quadratic, Koszul | ncGerst | |||
| noncommutative Gravity | ncGrav | 1, 1, 2, 4, 8, 16, 32 | OEIS: A011782 | lambda n: 1 if n == 1 else 2**(n-2) | dgvec | quadratic, Koszul | ncHyperCom | |
| noncommutative 2-Gerstenhaber | 2-ncGerst | 1, 1, 2, 3, 6, 10, 20 | OEIS: A001405 | binomial(n-1,(n-1)//2) | dgvec | quadratic | ||
| Directed Animals | DA | 1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046 | OEIS: A005773 | (1-3*x-(1-2*x-3*x**2).sqrt())/(6*x-2) | set | binary | ||
| Bol | Bol | 1, 1, 5 | vec | |||||
| Assosymetrique | AssoSym | 1, 2, 7, 29, 136, 762, 5139, 40539 | factorial(n)+2**n-binomial(n+1,2)-1 | vec | binary, quadratic, non-Koszul | |||
| column-convex polyominos | CoCoPoly | 1, 1, 3, 12, 54, 260, 1310, 6821, 36413 | set | free | ||||
| Tamari intervalles | Tamarint | 1, 1, 3, 13, 68, 399, 2530, 16965 | OEIS: A000260 | binomial(4*n - 2, n) / ((2*n - 1) * (3*n - 1)) | set | free | ||
| Free(NovExc) | Free(NovExc) | 1, 1, 3, 13, 66, 366, 2148, 13115 | OEIS: A219537 | x+x*(x/(1+x)**2/(1+x+x**2)).reverse() | set | free | ||
| Free(ModSyn) | Free(ModSyn) | 1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675, 1430715 | OEIS: A001764 | set | free | |||
| As(2) | As(2) | 1, 2, 4, 8, 16, 32 | OEIS: A000079 | 2**(n-1) | Zset | Koszul, binary, quadratic | As(2) | |
| As2 | As2 | 1, 2, 5, 14, 42, 132, 429, 1430, 4862 | OEIS: A000108 | binomial(2*n,n)/(n+1) | (x/(1+x)**2).reverse() | Zvec | Koszul, binary, quadratic, cyclic | |
| Nijenhuis | Nij | 1, 2 - t | dgvec | Koszul, binary, quadratic | ||||
| Structurable | Struc | 1, 0, 6, 0 | vec | ternary, quadratic | ||||
| Groupale | Gr | 2, 8, 48, 384 | OEIS: A000165 | factorial(n) * 2**n | set | |||
| Bessel | Bess | 1, 1-t, 1-3*t+3*t**2, 1-6*t+15*t**2-15*t**3 | dgvec | binary, quadratic, Hopf, Koszul | ||||
| Ramanujan | Ram | 1, 2 - t, 6 - 8*t + 3*t**2, 24 -58*t + 50*t**2 - 15*t**3 | ((1-t)*x/(1+x) + t*ln(1+x)).reverse() | dgvec | binary, quadratic, Hopf, Koszul | Ram! | ||
| Dual Ramanujan | Ram! | 1, 2-t | (1-t)*x/(1-x) - t*ln(1-x) | dgvec | binary, quadratic, Koszul | Ram | ||
| Di-alternative | DiAlt | 1, 4, 21, 72, 360 | vec | binary, quadratic, non-Koszul | ||||
| pre-Associative | PreAs | 1, 2, 6, 21, 80, 322, 1347, 5798, 25512, 114236 | OEIS: A106228 | set | binary, quadratic, non-Koszul | |||
| mock-dendriforme | mockDend | 1, 4, 30, 336, 5040 | OEIS: A001761 | factorial(n) * catalan_number(n) | Zvec | binary, quadratic, Koszul, cyclic | ||
| BinaryLie | BinLie | 1, 1, 3, 13, 75, 525, 4249 | vec | binary, cubic | ||||
| Sagle | Sagle | 1, 3, 11, 55, 330, 2345, 19088 | vec | binary, cubic | ||||
| Dual Lie-admissible | LieAdm! | 1, 2, 1, 1, 1, 1 | OEIS: A294619 | lambda n: 2 if n == 2 else 1 | x.exp()+x**2/2-1 | set | binary, quadratic, Koszul, monomial | LieAdm |
| Greg | Greg | 1, 3, 22, 262, 4336, 91984 | OEIS: A005264 | ((1+2*x)*(-x).exp()-1).reverse() | Zvec | binary, quadratic, Koszul, NielsenSchreier | Greg! | |
| Dual Greg | Greg! | 1, 3, 5, 7, 9, 11 | OEIS: A005408 | 2 * n - 1 | (2*x-1)*x.exp()+1 | Zvec | binary, quadratic, Koszul | Greg |
| Dual Alia | Alia! | 1, 2, 1, 0, 0, 0 | x+x**2+x**3/6 | vec | binary, quadratic, Koszul | Alia | ||
| Commutative Pre-Lie | ComPreLie | 1, 3, 19, 189, 2576, 44683 | OEIS: A052888 | (log(1+x)*exp(-x)).reverse() | Zvec | binary, quadratic | ||
| Lie-Griess | LieGriess | 1, 1 - t, 2 - 5*t + 3*t^2, 6 - 26*t + 35*t^2 - 15*t^3 | (-(1-t)*(exp(-x)-1)+x*t).reverse() | dgvec | binary, quadratic, Koszul | LieGriess! | ||
| Dual Lie-Griess | LieGriess! | 1, 1 - t, 1 - t, 1 - t | (1-t)*(exp(x)-1)+x*t | dgvec | binary, quadratic, Koszul | LieGriess | ||
| Flexible | Flex | 1, 2, 9, 61, 545, 5986 | OEIS: A370161 | vec | binary, quadratic, non-Koszul | |||
| Flexible Lie-Admissible | FlexLieAdm | 1, 2, 8, 48, 384, 3841 | OEIS: A370677 | vec | binary, quadratic, non-Koszul | |||
| CoupledNilpotent | CNilp | 1, 2, 1, 0, 0, 0, 0 | x * (1+x) * (1+x) | Zvec | binary, quadratic, Koszul, cyclic | CMag | ||
| CoupledMagmatic | CMag | 1, 2, 7, 30, 143, 728, 3876 | OEIS: A006013 | binomial(3*n-2,n-1)/n | (x * (1-x) * (1-x)).reverse() | Zvec | binary, quadratic, Koszul, cyclic | CNilp |
Operadia