details/L6n1_1_0_a25541f8.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(1/2, -1/2, -1/2) |
(1, 1, 1) |
x1^(-1/2)x2^(1/2)x3^(1/2) |
q^(0) |
{"0": [-1, 1, -1, -1], "1": [1, -1, 1, 1], "2": [-1, 1, -1, -1]}
|
|
(-1)*x1^(-1/2)*x2^(1/2)*x3^(1/2) + (-q^(-2))*x1^(-3/2)*x2^(3/2)*x3^(3/2) + (-q^(-6))*x1^(-5/2)*x2^(5/2)*x3^(5/2) + (-q^(-12))*x1^(-7/2)*x2^(7/2)*x3^(7/2) + (-q^(-20))*x1^(-9/2)*x2^(9/2)*x3^(9/2) + (-q^(-30))*x1^(-11/2)*x2^(11/2)*x3^(11/2)
|
(1/2, -1/2, -1/2) |
(1, 1, 1) |
x1^(-1/2)x2^(1/2)x3^(1/2) |
q^(0) |
{"0": [1, 1, -1, -1], "1": [1, 1, 1, 1], "2": [-1, 1, 1, -1]}
|
|
(-1)*x1^(-1/2)*x2^(1/2)*x3^(1/2) + (-q^(-2))*x1^(-3/2)*x2^(3/2)*x3^(3/2) + (-q^(-6))*x1^(-5/2)*x2^(5/2)*x3^(5/2) + (-q^(-12))*x1^(-7/2)*x2^(7/2)*x3^(7/2) + (-q^(-20))*x1^(-9/2)*x2^(9/2)*x3^(9/2) + (-q^(-30))*x1^(-11/2)*x2^(11/2)*x3^(11/2)
|
(-1/2, 1/2, 1/2) |
|
x1^(1/2)x2^(-1/2)x3^(-1/2) |
q^(0) |
|
|
(-1)*x1^(1/2)*x2^(-1/2)*x3^(-1/2) + (-q^(-2))*x1^(3/2)*x2^(-3/2)*x3^(-3/2) + (-q^(-6))*x1^(5/2)*x2^(-5/2)*x3^(-5/2) + (-q^(-12))*x1^(7/2)*x2^(-7/2)*x3^(-7/2) + (-q^(-20))*x1^(9/2)*x2^(-9/2)*x3^(-9/2) + (-q^(-30))*x1^(11/2)*x2^(-11/2)*x3^(-11/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, -2, 1, 2, -1, 2] |
3 |
6 |
3 |
Multivariable Alexander polynomial
| ΔL |
A1^(1/2)*A2^(-1/2)*A3^(-1/2) - A1^(-1/2)*A2^(1/2)*A3^(1/2) |
Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.
Interactive 3D view · hover a vertex for coordinates
Dual Thurston polytope
| Vertex | Dual to fibered face |
|---|
(1, -1, -1) |
yes |
(-1, 1, 1) |
yes |
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HFL polytope
| Poincaré polynomial |
|---|
m^(-3)*A2^(-1)*A3^(-1) + m^(-2)*A1^(-1) + m^(-2)*A2^(-1) + m^(-2)*A3^(-1) + m^(-2) + m^(-2)*A1*A2^(-1)*A3^(-1) + m^(-1)*A1^(-1)*A3 + m^(-1)*A1^(-1)*A2 + 3*m^(-1) + m^(-1)*A1*A2^(-1) + m^(-1)*A1*A3^(-1) + A1^(-1)*A2*A3 + A3 + A2 + A1 + m*A2*A3 |
| Vertex | Maslov | Rank |
|---|
(-1, 0, 0) | -2 | 1 |
(-1, 0, 1) | -1 | 1 |
(-1, 1, 0) | -1 | 1 |
(-1, 1, 1) | 0 | 1 |
(0, -1, -1) | -3 | 1 |
(0, -1, 0) | -2 | 1 |
(0, 0, -1) | -2 | 1 |
(0, 0, 1) | 0 | 1 |
(0, 1, 0) | 0 | 1 |
(0, 1, 1) | 1 | 1 |
(1, -1, -1) | -2 | 1 |
(1, -1, 0) | -1 | 1 |
(1, 0, -1) | -1 | 1 |
(1, 0, 0) | 0 | 1 |
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Record
FL/HFL Links
orderOption(int) |
39 |
|---|
namestring |
L6n1{1;0} |
|---|
statusstring |
success |
|---|
slugstring |
L6n1_1_0_a25541f8 |
|---|
result_filestring |
details/L6n1_1_0_a25541f8.json |
|---|
complexity_scoreOption(int) |
108 |
|---|
strandsOption(int) |
null |
|---|
crossingsOption(int) |
6 |
|---|
component_countOption(int) |
3 |
|---|
girthOption(int) |
6 |
|---|
total_rankOption(int) |
18 |
|---|
wall_secondsOption(float) |
0.00138 |
|---|
backend_secondsOption(float) |
0.0 |
|---|
errorstring |
|
|---|
dimensionOption(int) |
3 |
|---|
support_sizeOption(int) |
15 |
|---|
vertex_countOption(int) |
14 |
|---|
fibered_vertex_countOption(int) |
2 |
|---|
polytope_statusstring |
computed |
|---|
alexander_support_sizeOption(int) |
2 |
|---|
alexander_vertex_countOption(int) |
2 |
|---|
alexander_relationstring |
not_computed |
|---|
fk_countint |
3 |
|---|
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L6n1_1_0_a25541f8"
} |
|---|
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L6n1_1_0_a25541f8 |
|---|