details/L10n4_1_a4224c51.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^(3/2) |
{"0": [-1, 1, 1, 1], "1": [1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1]}
|
|
(-2*q^(-17/2) - 2*q^(-19/2) - 4*q^(-21/2))*x1^(-7/2)*x2^(17/2) + (-4*q^(-17/2) - 8*q^(-19/2) - 14*q^(-21/2) - 8*q^(-23/2) - 4*q^(-25/2) - 2*q^(-27/2))*x1^(-7/2)*x2^(19/2) + (-q^(-7/2) - 3*q^(-9/2))*x1^(-5/2)*x2^(13/2) + (-2*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-5/2)*x2^(15/2) + (q^(-5/2) - 13*q^(-9/2) - 11*q^(-11/2) - 9*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1^(-5/2)*x2^(17/2) + (-2*q^(-1/2) - 2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) - 14*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 10*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(-5/2)*x2^(19/2) + (-2*q^(-1/2))*x1^(-3/2)*x2^(9/2) + (-4*q^(-1/2) - 2*q^(-3/2))*x1^(-3/2)*x2^(11/2) + (2*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(-3/2)*x2^(13/2) + (-q^(5/2) + 4*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(-3/2)*x2^(15/2) + (-2*q^(7/2) - 6*q^(5/2) - 2*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-3/2)*x2^(17/2) + (q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 15*q^(5/2) - 8*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 6*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(19/2) + (-q^(3/2))*x1^(-1/2)*x2^(5/2) + (-2*q^(3/2))*x1^(-1/2)*x2^(7/2) + (q^(5/2) - 3*q^(3/2))*x1^(-1/2)*x2^(9/2) + (2*q^(5/2) - 4*q^(3/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(9/2) + 3*q^(5/2) - 5*q^(3/2))*x1^(-1/2)*x2^(13/2) + (-2*q^(11/2) - 4*q^(9/2) + 4*q^(5/2) - 6*q^(3/2))*x1^(-1/2)*x2^(15/2) + (2*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 6*q^(9/2) + 5*q^(5/2) - 7*q^(3/2))*x1^(-1/2)*x2^(17/2) + (2*q^(17/2) + 2*q^(15/2) - 4*q^(13/2) - 6*q^(11/2) - 8*q^(9/2) + 6*q^(5/2) - 8*q^(3/2))*x1^(-1/2)*x2^(19/2)
|
(1/2, -5/2) |
(1, 1) |
x1^(-1/2)x2^(5/2) |
q^(3/2) |
{"0": [1, 1, 1, 1], "1": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1]}
|
|
(-2*q^(-17/2) - 2*q^(-19/2) - 4*q^(-21/2))*x1^(-7/2)*x2^(17/2) + (-4*q^(-17/2) - 8*q^(-19/2) - 14*q^(-21/2) - 8*q^(-23/2) - 4*q^(-25/2) - 2*q^(-27/2))*x1^(-7/2)*x2^(19/2) + (-q^(-7/2) - 3*q^(-9/2))*x1^(-5/2)*x2^(13/2) + (-2*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-5/2)*x2^(15/2) + (q^(-5/2) - 13*q^(-9/2) - 11*q^(-11/2) - 9*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1^(-5/2)*x2^(17/2) + (-2*q^(-1/2) - 2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) - 14*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 10*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(-5/2)*x2^(19/2) + (-2*q^(-1/2))*x1^(-3/2)*x2^(9/2) + (-4*q^(-1/2) - 2*q^(-3/2))*x1^(-3/2)*x2^(11/2) + (2*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(-3/2)*x2^(13/2) + (-q^(5/2) + 4*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(-3/2)*x2^(15/2) + (-2*q^(7/2) - 6*q^(5/2) - 2*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-3/2)*x2^(17/2) + (q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 15*q^(5/2) - 8*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 6*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(19/2) + (-q^(3/2))*x1^(-1/2)*x2^(5/2) + (-2*q^(3/2))*x1^(-1/2)*x2^(7/2) + (q^(5/2) - 3*q^(3/2))*x1^(-1/2)*x2^(9/2) + (2*q^(5/2) - 4*q^(3/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(9/2) + 3*q^(5/2) - 5*q^(3/2))*x1^(-1/2)*x2^(13/2) + (-2*q^(11/2) - 4*q^(9/2) + 4*q^(5/2) - 6*q^(3/2))*x1^(-1/2)*x2^(15/2) + (2*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 6*q^(9/2) + 5*q^(5/2) - 7*q^(3/2))*x1^(-1/2)*x2^(17/2) + (2*q^(17/2) + 2*q^(15/2) - 4*q^(13/2) - 6*q^(11/2) - 8*q^(9/2) + 6*q^(5/2) - 8*q^(3/2))*x1^(-1/2)*x2^(19/2)
|
(-1/2, 5/2) |
|
x1^(1/2)x2^(-5/2) |
q^(3/2) |
|
|
(-2*q^(-17/2) - 2*q^(-19/2) - 4*q^(-21/2))*x1^(7/2)*x2^(-17/2) + (-4*q^(-17/2) - 8*q^(-19/2) - 14*q^(-21/2) - 8*q^(-23/2) - 4*q^(-25/2) - 2*q^(-27/2))*x1^(7/2)*x2^(-19/2) + (-q^(-7/2) - 3*q^(-9/2))*x1^(5/2)*x2^(-13/2) + (-2*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(5/2)*x2^(-15/2) + (q^(-5/2) - 13*q^(-9/2) - 11*q^(-11/2) - 9*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1^(5/2)*x2^(-17/2) + (-2*q^(-1/2) - 2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2) - 14*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 10*q^(-15/2) - 6*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(5/2)*x2^(-19/2) + (-2*q^(-1/2))*x1^(3/2)*x2^(-9/2) + (-4*q^(-1/2) - 2*q^(-3/2))*x1^(3/2)*x2^(-11/2) + (2*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(3/2)*x2^(-13/2) + (-q^(5/2) + 4*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(3/2)*x2^(-15/2) + (-2*q^(7/2) - 6*q^(5/2) - 2*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(3/2)*x2^(-17/2) + (q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 15*q^(5/2) - 8*q^(3/2) + 6*q^(1/2) - 6*q^(-1/2) - 6*q^(-3/2) - 6*q^(-5/2) - 6*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(3/2)*x2^(-19/2) + (-q^(3/2))*x1^(1/2)*x2^(-5/2) + (-2*q^(3/2))*x1^(1/2)*x2^(-7/2) + (q^(5/2) - 3*q^(3/2))*x1^(1/2)*x2^(-9/2) + (2*q^(5/2) - 4*q^(3/2))*x1^(1/2)*x2^(-11/2) + (-2*q^(9/2) + 3*q^(5/2) - 5*q^(3/2))*x1^(1/2)*x2^(-13/2) + (-2*q^(11/2) - 4*q^(9/2) + 4*q^(5/2) - 6*q^(3/2))*x1^(1/2)*x2^(-15/2) + (2*q^(15/2) - 2*q^(13/2) - 4*q^(11/2) - 6*q^(9/2) + 5*q^(5/2) - 7*q^(3/2))*x1^(1/2)*x2^(-17/2) + (2*q^(17/2) + 2*q^(15/2) - 4*q^(13/2) - 6*q^(11/2) - 8*q^(9/2) + 6*q^(5/2) - 8*q^(3/2))*x1^(1/2)*x2^(-19/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, 2, -1, 2, 1, 3, -2, 3, 3, 3] |
2 |
10 |
4 |
Multivariable Alexander polynomial
| ΔL |
2*A1^(1/2)*A2^(1/2) - 2*A1^(1/2)*A2^(-1/2) + 2*A1^(1/2)*A2^(-3/2) - A1^(1/2)*A2^(-5/2) - A1^(-1/2)*A2^(5/2) + 2*A1^(-1/2)*A2^(3/2) - 2*A1^(-1/2)*A2^(1/2) + 2*A1^(-1/2)*A2^(-1/2) |
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, -1) |
no |
(1, -5) |
yes |
(1, 1) |
no |
(-1, 5) |
yes |
HFL polytope
| Poincaré polynomial |
m^(-5)*A2^(-3) + 2*m^(-4)*A1^(-1)*A2^(-1) + 3*m^(-4)*A2^(-2) + m^(-4)*A1*A2^(-3) + 4*m^(-3)*A1^(-1) + 6*m^(-3)*A2^(-1) + 3*m^(-3)*A1*A2^(-2) + 4*m^(-2)*A1^(-1)*A2 + 8*m^(-2) + 4*m^(-2)*A1*A2^(-1) + 3*m^(-1)*A1^(-1)*A2^2 + 6*m^(-1)*A2 + 4*m^(-1)*A1 + A1^(-1)*A2^3 + 3*A2^2 + 2*A1*A2 + m*A2^3 |
| Vertex | Maslov | Rank |
(-1, -1) | -4 | 2 |
(0, -3) | -5 | 1 |
(1, -3) | -4 | 1 |
(1, 1) | 0 | 2 |
(0, 3) | 1 | 1 |
(-1, 3) | 0 | 1 |
Record
FL/HFL Links
orderOption(int) |
568 |
namestring |
L10n4{1} |
statusstring |
success |
slugstring |
L10n4_1_a4224c51 |
result_filestring |
details/L10n4_1_a4224c51.json |
complexity_scoreOption(int) |
200 |
strandsOption(int) |
null |
crossingsOption(int) |
10 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
56 |
wall_secondsOption(float) |
0.003134 |
backend_secondsOption(float) |
0.0 |
errorstring |
|
dimensionOption(int) |
2 |
support_sizeOption(int) |
17 |
vertex_countOption(int) |
6 |
fibered_vertex_countOption(int) |
2 |
polytope_statusstring |
computed |
alexander_support_sizeOption(int) |
8 |
alexander_vertex_countOption(int) |
4 |
alexander_relationstring |
not_computed |
fk_countint |
2 |
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L10n4_1_a4224c51"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10n4_1_a4224c51 |