details/L10n10_0_a5007b52.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^(-5/2) |
{"0": [-1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1], "1": [1, -1, -1, -1, -1, -1]}
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(-q^(-5/2))*x1^(1/2)*x2^(5/2) + (-2*q^(-5/2))*x1^(1/2)*x2^(7/2) + (-q^(-3/2) - 3*q^(-5/2))*x1^(1/2)*x2^(9/2) + (-2*q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2))*x1^(1/2)*x2^(11/2) + (-q^(3/2) - 3*q^(1/2) - 4*q^(-1/2) - 3*q^(-3/2) - 5*q^(-5/2))*x1^(1/2)*x2^(13/2) + (-2*q^(-13/2))*x1^(3/2)*x2^(13/2) + (-2*q^(7/2) - 2*q^(5/2) - 6*q^(3/2) - 6*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 6*q^(-5/2))*x1^(1/2)*x2^(15/2) + (-q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(3/2)*x2^(15/2) + (-q^(13/2) - 3*q^(11/2) - 4*q^(9/2) - 7*q^(7/2) - 9*q^(5/2) - 11*q^(3/2) - 9*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - 7*q^(-5/2))*x1^(1/2)*x2^(17/2) + (-2*q^(-9/2) - 4*q^(-11/2) - 8*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(3/2)*x2^(17/2) + (-2*q^(19/2) - 2*q^(17/2) - 6*q^(15/2) - 8*q^(13/2) - 12*q^(11/2) - 12*q^(9/2) - 18*q^(7/2) - 16*q^(5/2) - 16*q^(3/2) - 12*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) - 8*q^(-5/2))*x1^(1/2)*x2^(19/2) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 11*q^(-11/2) - 14*q^(-13/2) - 8*q^(-15/2) - 4*q^(-17/2) - 2*q^(-19/2))*x1^(3/2)*x2^(19/2)
|
(-1/2, -5/2) |
(1, 1) |
x1^(1/2)x2^(5/2) |
q^(-5/2) |
{"0": [1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1], "1": [1, 1, -1, -1, -1, -1]}
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(-q^(-5/2))*x1^(1/2)*x2^(5/2) + (-2*q^(-5/2))*x1^(1/2)*x2^(7/2) + (-q^(-3/2) - 3*q^(-5/2))*x1^(1/2)*x2^(9/2) + (-2*q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2))*x1^(1/2)*x2^(11/2) + (-q^(3/2) - 3*q^(1/2) - 4*q^(-1/2) - 3*q^(-3/2) - 5*q^(-5/2))*x1^(1/2)*x2^(13/2) + (-2*q^(-13/2))*x1^(3/2)*x2^(13/2) + (-2*q^(7/2) - 2*q^(5/2) - 6*q^(3/2) - 6*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 6*q^(-5/2))*x1^(1/2)*x2^(15/2) + (-q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(3/2)*x2^(15/2) + (-q^(13/2) - 3*q^(11/2) - 4*q^(9/2) - 7*q^(7/2) - 9*q^(5/2) - 11*q^(3/2) - 9*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - 7*q^(-5/2))*x1^(1/2)*x2^(17/2) + (-2*q^(-9/2) - 4*q^(-11/2) - 8*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(3/2)*x2^(17/2) + (-2*q^(19/2) - 2*q^(17/2) - 6*q^(15/2) - 8*q^(13/2) - 12*q^(11/2) - 12*q^(9/2) - 18*q^(7/2) - 16*q^(5/2) - 16*q^(3/2) - 12*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) - 8*q^(-5/2))*x1^(1/2)*x2^(19/2) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 11*q^(-11/2) - 14*q^(-13/2) - 8*q^(-15/2) - 4*q^(-17/2) - 2*q^(-19/2))*x1^(3/2)*x2^(19/2)
|
(1/2, 5/2) |
|
x1^(-1/2)x2^(-5/2) |
q^(-5/2) |
|
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(-q^(-5/2))*x1^(-1/2)*x2^(-5/2) + (-2*q^(-5/2))*x1^(-1/2)*x2^(-7/2) + (-q^(-3/2) - 3*q^(-5/2))*x1^(-1/2)*x2^(-9/2) + (-2*q^(-1/2) - 2*q^(-3/2) - 4*q^(-5/2))*x1^(-1/2)*x2^(-11/2) + (-q^(3/2) - 3*q^(1/2) - 4*q^(-1/2) - 3*q^(-3/2) - 5*q^(-5/2))*x1^(-1/2)*x2^(-13/2) + (-2*q^(-13/2))*x1^(-3/2)*x2^(-13/2) + (-2*q^(7/2) - 2*q^(5/2) - 6*q^(3/2) - 6*q^(1/2) - 6*q^(-1/2) - 4*q^(-3/2) - 6*q^(-5/2))*x1^(-1/2)*x2^(-15/2) + (-q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-3/2)*x2^(-15/2) + (-q^(13/2) - 3*q^(11/2) - 4*q^(9/2) - 7*q^(7/2) - 9*q^(5/2) - 11*q^(3/2) - 9*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - 7*q^(-5/2))*x1^(-1/2)*x2^(-17/2) + (-2*q^(-9/2) - 4*q^(-11/2) - 8*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(19/2) - 2*q^(17/2) - 6*q^(15/2) - 8*q^(13/2) - 12*q^(11/2) - 12*q^(9/2) - 18*q^(7/2) - 16*q^(5/2) - 16*q^(3/2) - 12*q^(1/2) - 10*q^(-1/2) - 6*q^(-3/2) - 8*q^(-5/2))*x1^(-1/2)*x2^(-19/2) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 11*q^(-11/2) - 14*q^(-13/2) - 8*q^(-15/2) - 4*q^(-17/2) - 2*q^(-19/2))*x1^(-3/2)*x2^(-19/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[1, 2, -3, 2, -1, -3, -2, -3, -2, -3, -2, -3] |
2 |
12 |
4 |
Multivariable Alexander polynomial
| ΔL |
A1^(1/2)*A2^(5/2) - 2*A1^(1/2)*A2^(3/2) - 2*A1^(-1/2)*A2^(-3/2) + 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, -3) |
no |
(-1, -5) |
yes |
(1, 3) |
no |
(1, 5) |
yes |
HFL polytope
| Poincaré polynomial |
|---|
m^(-2)*A1^(-1)*A2^(-3) + 3*m^(-1)*A1^(-1)*A2^(-2) + m^(-1)*A2^(-3) + 2*A1^(-1)*A2^(-1) + 3*A2^(-2) + A2^(-1) + 3*m*A2^(-1) + 3*m + 3*m^2 + m^2*A2 + 3*m^3*A2 + 3*m^4*A2^2 + 2*m^4*A1*A2 + m^5*A2^3 + 3*m^5*A1*A2^2 + m^6*A1*A2^3 |
| Vertex | Maslov | Rank |
|---|
(-1, -3) | -2 | 1 |
(0, -3) | -1 | 1 |
(1, 1) | 4 | 2 |
(1, 3) | 6 | 1 |
(0, 3) | 5 | 1 |
(-1, -1) | 0 | 2 |
Record
FL/HFL Links
orderOption(int) |
481 |
|---|
namestring |
L10n10{0} |
|---|
statusstring |
success |
|---|
slugstring |
L10n10_0_a5007b52 |
|---|
result_filestring |
details/L10n10_0_a5007b52.json |
|---|
complexity_scoreOption(int) |
200 |
|---|
strandsOption(int) |
null |
|---|
crossingsOption(int) |
10 |
|---|
component_countOption(int) |
2 |
|---|
girthOption(int) |
6 |
|---|
total_rankOption(int) |
34 |
|---|
wall_secondsOption(float) |
0.001642 |
|---|
backend_secondsOption(float) |
0.0 |
|---|
errorstring |
|
|---|
dimensionOption(int) |
2 |
|---|
support_sizeOption(int) |
13 |
|---|
vertex_countOption(int) |
6 |
|---|
fibered_vertex_countOption(int) |
2 |
|---|
polytope_statusstring |
computed |
|---|
alexander_support_sizeOption(int) |
4 |
|---|
alexander_vertex_countOption(int) |
4 |
|---|
alexander_relationstring |
not_computed |
|---|
fk_countint |
2 |
|---|
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L10n10_0_a5007b52"
} |
|---|
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10n10_0_a5007b52 |
|---|