details/L9n4_1_d0d83011.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]}
 
(q^(-13/2))*x1^(-3/2)*x2^(15/2) + (-q^(-3/2))*x1^(-1/2)*x2^(5/2)
(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]}
 
(q^(-13/2))*x1^(-3/2)*x2^(15/2) + (-q^(-3/2))*x1^(-1/2)*x2^(5/2)
(-1/2, 5/2) x1^(1/2)x2^(-5/2) q^(-3/2) 
(q^(-13/2))*x1^(3/2)*x2^(-15/2) + (-q^(-3/2))*x1^(1/2)*x2^(-5/2)

Braid

Braid word Components Crossings Strands
[1, 2, -1, 2, 1, -2, -2, -2, -2] 2 9 3

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(-5/2) + 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.

Newton Polygon of Alexander-0.500.5-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, 5) yes
(1, -5) yes
Dual Thurston polygon-101-505h1h2

HFL polytope

Poincaré polynomial
m^(-2)*A2^(-3) + m^(-1)*A2^(-2) + m^(-1)*A2^(-1) + m^(-1)*A1*A2^(-3) + A2^(-1) + 1 + A1*A2^(-2) + m + m*A2 + m^2*A1^(-1)*A2^2 + m^2*A2 + m^3*A1^(-1)*A2^3 + m^3*A2^2 + m^4*A2^3
VertexMaslovRank
(-1, 2)21
(0, -3)-21
(1, -3)-11
(1, -2)01
(0, 3)41
(-1, 3)31
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 188
namestring L9n4{1}
statusstring success
slugstring L9n4_1_d0d83011
result_filestring details/L9n4_1_d0d83011.json
complexity_scoreOption(int) 162
strandsOption(int) null
crossingsOption(int) 9
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 14
wall_secondsOption(float) 0.002859
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 11
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": "L9n4_1_d0d83011"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L9n4_1_d0d83011