details/L4a1_1_8073566d.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, -1/2) (1, 1) x1^(1/2)x2^(1/2) q^(3/2) 
{"0": [-1, 1, -1, 1], "1": [1, -1, 1, -1]}
 
(-q^(3/2))*x1^(1/2)*x2^(1/2) + (q^(5/2))*x1^(3/2)*x2^(3/2) + (-q^(9/2))*x1^(5/2)*x2^(5/2) + (q^(15/2))*x1^(7/2)*x2^(7/2) + (-q^(23/2))*x1^(9/2)*x2^(9/2) + (q^(33/2))*x1^(11/2)*x2^(11/2) + (-q^(45/2))*x1^(13/2)*x2^(13/2) + (q^(59/2))*x1^(15/2)*x2^(15/2) + (-q^(75/2))*x1^(17/2)*x2^(17/2) + (q^(93/2))*x1^(19/2)*x2^(19/2)
(-1/2, -1/2) (1, 1) x1^(1/2)x2^(1/2) q^(3/2) 
{"0": [1, 1, 1, 1], "1": [1, 1, 1, 1]}
 
(-q^(3/2))*x1^(1/2)*x2^(1/2) + (q^(5/2))*x1^(3/2)*x2^(3/2) + (-q^(9/2))*x1^(5/2)*x2^(5/2) + (q^(15/2))*x1^(7/2)*x2^(7/2) + (-q^(23/2))*x1^(9/2)*x2^(9/2) + (q^(33/2))*x1^(11/2)*x2^(11/2) + (-q^(45/2))*x1^(13/2)*x2^(13/2) + (q^(59/2))*x1^(15/2)*x2^(15/2) + (-q^(75/2))*x1^(17/2)*x2^(17/2) + (q^(93/2))*x1^(19/2)*x2^(19/2)
(1/2, 1/2) x1^(-1/2)x2^(-1/2) q^(3/2) 
(-q^(3/2))*x1^(-1/2)*x2^(-1/2) + (q^(5/2))*x1^(-3/2)*x2^(-3/2) + (-q^(9/2))*x1^(-5/2)*x2^(-5/2) + (q^(15/2))*x1^(-7/2)*x2^(-7/2) + (-q^(23/2))*x1^(-9/2)*x2^(-9/2) + (q^(33/2))*x1^(-11/2)*x2^(-11/2) + (-q^(45/2))*x1^(-13/2)*x2^(-13/2) + (q^(59/2))*x1^(-15/2)*x2^(-15/2) + (-q^(75/2))*x1^(-17/2)*x2^(-17/2) + (q^(93/2))*x1^(-19/2)*x2^(-19/2)

Braid

Braid word Components Crossings Strands
[1, 1, 1, 1] 2 4 2

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(1/2) + 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.

Newton Polygon of Alexander-0.500.5-0.500.5A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, -1) yes
(1, 1) yes
Dual Thurston polygon-101-101h1h2

HFL polytope

Poincaré polynomial
m^(-4)*A1^(-1)*A2^(-1) + m^(-3)*A1^(-1) + m^(-3)*A2^(-1) + 2*m^(-2) + m^(-1)*A2 + m^(-1)*A1 + A1*A2
VertexMaslovRank
(-1, -1)-41
(0, -1)-31
(1, 0)-11
(1, 1)01
(0, 1)-11
(-1, 0)-31
HFL polytope-101-101A1A2

Record

FL/HFL Links

orderOption(int) 4
namestring L4a1{1}
statusstring success
slugstring L4a1_1_8073566d
result_filestring details/L4a1_1_8073566d.json
complexity_scoreOption(int) 32
strandsOption(int) null
crossingsOption(int) 4
component_countOption(int) 2
girthOption(int) 4
total_rankOption(int) 8
wall_secondsOption(float) 0.002638
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 7
vertex_countOption(int) 6
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": "L4a1_1_8073566d"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L4a1_1_8073566d