details/L8n3_1_1_cb567165.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1/2, -1, -1) (1, 1, 1) x1^(-1/2)x2^(1)x3^(1) q^(-1) 
{"0": [-1, 1, 1, 1], "1": [1, -1, -1, -1, 1, -1], "2": [-1, -1, -1, 1, -1, 1]}
 
(-q^(-13))*x1^(-5/2)*x2^(5)*x3^(5) + (-q^(-5))*x1^(-3/2)*x2^(3)*x3^(3) + (-q^(-1))*x1^(-1/2)*x2*x3
(1/2, -1, -1) (1, 1, 1) x1^(-1/2)x2^(1)x3^(1) q^(-1) 
{"0": [1, 1, 1, 1], "1": [1, 1, -1, -1, 1, -1], "2": [-1, -1, 1, 1, -1, 1]}
 
(-q^(-13))*x1^(-5/2)*x2^(5)*x3^(5) + (-q^(-5))*x1^(-3/2)*x2^(3)*x3^(3) + (-q^(-1))*x1^(-1/2)*x2*x3
(-1/2, 1, 1) x1^(1/2)x2^(-1)x3^(-1) q^(-1) 
(-q^(-13))*x1^(5/2)*x2^(-5)*x3^(-5) + (-q^(-5))*x1^(3/2)*x2^(-3)*x3^(-3) + (-q^(-1))*x1^(1/2)*x2^(-1)*x3^(-1)

Braid

Braid word Components Crossings Strands
[1, 2, -1, 2, 1, -2, -2, -2] 3 8 3

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(-1)*A3^(-1) - A1^(-1/2)*A2*A3

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

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Dual Thurston polytope

VertexDual to fibered face
(-1, 2, 2) yes
(1, -2, -2) yes
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HFL polytope

Poincaré polynomial
m^(-3)*A2^(-3/2)*A3^(-3/2) + m^(-2)*A2^(-3/2)*A3^(-1/2) + m^(-2)*A2^(-1/2)*A3^(-3/2) + m^(-2)*A2^(-1/2)*A3^(-1/2) + m^(-2)*A1*A2^(-3/2)*A3^(-3/2) + 2*m^(-1)*A2^(-1/2)*A3^(-1/2) + m^(-1)*A2^(-1/2)*A3^(1/2) + m^(-1)*A2^(1/2)*A3^(-1/2) + m^(-1)*A1*A2^(-3/2)*A3^(-1/2) + m^(-1)*A1*A2^(-1/2)*A3^(-3/2) + A1^(-1)*A2^(1/2)*A3^(1/2) + A2^(-1/2)*A3^(1/2) + A2^(1/2)*A3^(-1/2) + A2^(1/2)*A3^(1/2) + A1*A2^(-1/2)*A3^(-1/2) + m*A1^(-1)*A2^(1/2)*A3^(3/2) + m*A1^(-1)*A2^(3/2)*A3^(1/2) + 2*m*A2^(1/2)*A3^(1/2) + m^2*A1^(-1)*A2^(3/2)*A3^(3/2) + m^2*A2^(1/2)*A3^(3/2) + m^2*A2^(3/2)*A3^(1/2) + m^3*A2^(3/2)*A3^(3/2)
VertexMaslovRank
(-1, 1/2, 1/2)01
(-1, 1/2, 3/2)11
(-1, 3/2, 1/2)11
(-1, 3/2, 3/2)21
(0, -3/2, -3/2)-31
(0, -3/2, -1/2)-21
(0, -1/2, -3/2)-21
(0, 1/2, 3/2)21
(0, 3/2, 1/2)21
(0, 3/2, 3/2)31
(1, -3/2, -3/2)-21
(1, -3/2, -1/2)-11
(1, -1/2, -3/2)-11
(1, -1/2, -1/2)01
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Record

FL/HFL Links

orderOption(int) 226
namestring L8n3{1;1}
statusstring success
slugstring L8n3_1_1_cb567165
result_filestring details/L8n3_1_1_cb567165.json
complexity_scoreOption(int) 192
strandsOption(int) null
crossingsOption(int) 8
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 24
wall_secondsOption(float) 0.002713
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 18
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": "L8n3_1_1_cb567165"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L8n3_1_1_cb567165