details/L9n12_1_d9ba2e15.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(-1/2, -5/2) |
(1, 1) |
x1^(1/2)x2^(5/2) |
q^(7/2) |
{"0": [-1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1], "1": [1, 1, 1, 1]}
|
|
(-q^(7/2))*x1^(1/2)*x2^(5/2) + (-q^(9/2))*x1^(1/2)*x2^(9/2) + (q^(11/2))*x1^(3/2)*x2^(9/2) + (q^(11/2))*x1^(1/2)*x2^(11/2) + (-q^(13/2))*x1^(3/2)*x2^(11/2) + (-q^(11/2))*x1^(1/2)*x2^(13/2) + (q^(17/2) + q^(15/2))*x1^(3/2)*x2^(13/2) + (-q^(17/2))*x1^(5/2)*x2^(13/2) + (q^(15/2) + q^(13/2))*x1^(1/2)*x2^(15/2) + (-2*q^(19/2) - q^(17/2))*x1^(3/2)*x2^(15/2) + (q^(21/2) + q^(19/2))*x1^(5/2)*x2^(15/2) + (-q^(17/2) - q^(13/2))*x1^(1/2)*x2^(17/2) + (2*q^(23/2) + 2*q^(21/2) + q^(19/2))*x1^(3/2)*x2^(17/2) + (-q^(27/2) - q^(25/2) - 2*q^(23/2))*x1^(5/2)*x2^(17/2) + (q^(25/2))*x1^(7/2)*x2^(17/2) + (q^(19/2) + q^(17/2) + q^(15/2))*x1^(1/2)*x2^(19/2) + (-q^(27/2) - 3*q^(25/2) - 2*q^(23/2) - q^(21/2))*x1^(3/2)*x2^(19/2) + (q^(31/2) + 3*q^(29/2) + 2*q^(27/2) + q^(25/2))*x1^(5/2)*x2^(19/2) + (-q^(31/2) - q^(29/2) - q^(27/2))*x1^(7/2)*x2^(19/2)
|
(-1/2, -5/2) |
(1, 1) |
x1^(1/2)x2^(5/2) |
q^(7/2) |
{"0": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1]}
|
|
(-q^(7/2))*x1^(1/2)*x2^(5/2) + (-q^(9/2))*x1^(1/2)*x2^(9/2) + (q^(11/2))*x1^(3/2)*x2^(9/2) + (q^(11/2))*x1^(1/2)*x2^(11/2) + (-q^(13/2))*x1^(3/2)*x2^(11/2) + (-q^(11/2))*x1^(1/2)*x2^(13/2) + (q^(17/2) + q^(15/2))*x1^(3/2)*x2^(13/2) + (-q^(17/2))*x1^(5/2)*x2^(13/2) + (q^(15/2) + q^(13/2))*x1^(1/2)*x2^(15/2) + (-2*q^(19/2) - q^(17/2))*x1^(3/2)*x2^(15/2) + (q^(21/2) + q^(19/2))*x1^(5/2)*x2^(15/2) + (-q^(17/2) - q^(13/2))*x1^(1/2)*x2^(17/2) + (2*q^(23/2) + 2*q^(21/2) + q^(19/2))*x1^(3/2)*x2^(17/2) + (-q^(27/2) - q^(25/2) - 2*q^(23/2))*x1^(5/2)*x2^(17/2) + (q^(25/2))*x1^(7/2)*x2^(17/2) + (q^(19/2) + q^(17/2) + q^(15/2))*x1^(1/2)*x2^(19/2) + (-q^(27/2) - 3*q^(25/2) - 2*q^(23/2) - q^(21/2))*x1^(3/2)*x2^(19/2) + (q^(31/2) + 3*q^(29/2) + 2*q^(27/2) + q^(25/2))*x1^(5/2)*x2^(19/2) + (-q^(31/2) - q^(29/2) - q^(27/2))*x1^(7/2)*x2^(19/2)
|
(1/2, 5/2) |
|
x1^(-1/2)x2^(-5/2) |
q^(7/2) |
|
|
(-q^(7/2))*x1^(-1/2)*x2^(-5/2) + (-q^(9/2))*x1^(-1/2)*x2^(-9/2) + (q^(11/2))*x1^(-3/2)*x2^(-9/2) + (q^(11/2))*x1^(-1/2)*x2^(-11/2) + (-q^(13/2))*x1^(-3/2)*x2^(-11/2) + (-q^(11/2))*x1^(-1/2)*x2^(-13/2) + (q^(17/2) + q^(15/2))*x1^(-3/2)*x2^(-13/2) + (-q^(17/2))*x1^(-5/2)*x2^(-13/2) + (q^(15/2) + q^(13/2))*x1^(-1/2)*x2^(-15/2) + (-2*q^(19/2) - q^(17/2))*x1^(-3/2)*x2^(-15/2) + (q^(21/2) + q^(19/2))*x1^(-5/2)*x2^(-15/2) + (-q^(17/2) - q^(13/2))*x1^(-1/2)*x2^(-17/2) + (2*q^(23/2) + 2*q^(21/2) + q^(19/2))*x1^(-3/2)*x2^(-17/2) + (-q^(27/2) - q^(25/2) - 2*q^(23/2))*x1^(-5/2)*x2^(-17/2) + (q^(25/2))*x1^(-7/2)*x2^(-17/2) + (q^(19/2) + q^(17/2) + q^(15/2))*x1^(-1/2)*x2^(-19/2) + (-q^(27/2) - 3*q^(25/2) - 2*q^(23/2) - q^(21/2))*x1^(-3/2)*x2^(-19/2) + (q^(31/2) + 3*q^(29/2) + 2*q^(27/2) + q^(25/2))*x1^(-5/2)*x2^(-19/2) + (-q^(31/2) - q^(29/2) - q^(27/2))*x1^(-7/2)*x2^(-19/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, 1, 2, 2, 1, 1, 2, 2, 1] |
2 |
9 |
3 |
Multivariable Alexander polynomial
| ΔL |
A1^(1/2)*A2^(5/2) - A1^(1/2)*A2^(1/2) + A1^(1/2)*A2^(-1/2) + A1^(-1/2)*A2^(1/2) - A1^(-1/2)*A2^(-1/2) + A1^(-1/2)*A2^(-5/2) |
Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.
Dual Thurston polytope
| Vertex | Dual to fibered face |
|---|
(-1, -5) |
yes |
(1, -1) |
yes |
(1, 5) |
yes |
(-1, 1) |
yes |
HFL polytope
| Poincaré polynomial |
|---|
m^(-8)*A1^(-1)*A2^(-3) + m^(-7)*A1^(-1)*A2^(-2) + m^(-7)*A2^(-3) + m^(-6)*A2^(-2) + m^(-5)*A1^(-1)*A2^(-1) + 2*m^(-4)*A1^(-1) + 2*m^(-4)*A2^(-1) + m^(-3)*A1^(-1)*A2 + 4*m^(-3) + m^(-3)*A1*A2^(-1) + 2*m^(-2)*A2 + m^(-2)*A2^2 + 2*m^(-2)*A1 + m^(-1)*A2^3 + m^(-1)*A1*A2 + m^(-1)*A1*A2^2 + A1*A2^3 |
| Vertex | Maslov | Rank |
|---|
(-1, -3) | -8 | 1 |
(0, -3) | -7 | 1 |
(1, -1) | -3 | 1 |
(1, 3) | 0 | 1 |
(0, 3) | -1 | 1 |
(-1, 1) | -3 | 1 |
Record
FL/HFL Links
orderOption(int) |
166 |
|---|
namestring |
L9n12{1} |
|---|
statusstring |
success |
|---|
slugstring |
L9n12_1_d9ba2e15 |
|---|
result_filestring |
details/L9n12_1_d9ba2e15.json |
|---|
complexity_scoreOption(int) |
162 |
|---|
strandsOption(int) |
null |
|---|
crossingsOption(int) |
9 |
|---|
component_countOption(int) |
2 |
|---|
girthOption(int) |
6 |
|---|
total_rankOption(int) |
24 |
|---|
wall_secondsOption(float) |
0.001865 |
|---|
backend_secondsOption(float) |
0.0 |
|---|
errorstring |
|
|---|
dimensionOption(int) |
2 |
|---|
support_sizeOption(int) |
17 |
|---|
vertex_countOption(int) |
6 |
|---|
fibered_vertex_countOption(int) |
4 |
|---|
polytope_statusstring |
computed |
|---|
alexander_support_sizeOption(int) |
6 |
|---|
alexander_vertex_countOption(int) |
4 |
|---|
alexander_relationstring |
not_computed |
|---|
fk_countint |
3 |
|---|
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L9n12_1_d9ba2e15"
} |
|---|
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L9n12_1_d9ba2e15 |
|---|