details/L9n15_1_c54732ae.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1, -2) (1, 1) x1^(-1)x2^(2) q^(-1/2) 
{"0": [-1, 1, 1, 1, 1, 1], "1": [1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1]}
 
(-q^(-21/2))*x1^(-4)*x2^(8) + (q^(-5/2))*x1^(-2)*x2^(4) + (-q^(-1/2))*x1^(-1)*x2^(2)
(1, -2) (1, 1) x1^(-1)x2^(2) q^(-1/2) 
{"0": [1, 1, 1, 1, 1, 1], "1": [1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1]}
 
(-q^(-21/2))*x1^(-4)*x2^(8) + (q^(-5/2))*x1^(-2)*x2^(4) + (-q^(-1/2))*x1^(-1)*x2^(2)
(-1, 2) x1^(1)x2^(-2) q^(-1/2) 
(-q^(-21/2))*x1^(4)*x2^(-8) + (q^(-5/2))*x1^(2)*x2^(-4) + (-q^(-1/2))*x1*x2^(-2)

Braid

Braid word Components Crossings Strands
[1, 2, -1, 3, -2, 3, 2, 1, -2, -3] 2 10 4

Multivariable Alexander polynomial

ΔL
A1*A2^(-2) + 1 + A1^(-1)*A2^(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-101-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-2, 4) yes
(2, -4) yes
Dual Thurston polygon-202-505h1h2

HFL polytope

Poincaré polynomial
m^(-2)*A1^(-1/2)*A2^(-1/2) + m^(-2)*A1^(1/2)*A2^(-5/2) + m^(-1)*A1^(-1/2)*A2^(1/2) + m^(-1)*A1^(1/2)*A2^(-3/2) + m^(-1)*A1^(1/2)*A2^(-1/2) + m^(-1)*A1^(3/2)*A2^(-5/2) + A1^(-3/2)*A2^(3/2) + A1^(1/2)*A2^(1/2) + A1^(3/2)*A2^(-3/2) + m*A1^(-3/2)*A2^(5/2) + m*A1^(-1/2)*A2^(3/2) + m^2*A1^(-1/2)*A2^(5/2)
VertexMaslovRank
(-3/2, 3/2)01
(1/2, -5/2)-21
(3/2, -5/2)-11
(3/2, -3/2)01
(-1/2, 5/2)21
(-3/2, 5/2)11
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 172
namestring L9n15{1}
statusstring success
slugstring L9n15_1_c54732ae
result_filestring details/L9n15_1_c54732ae.json
complexity_scoreOption(int) 162
strandsOption(int) null
crossingsOption(int) 9
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 12
wall_secondsOption(float) 0.001549
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 12
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 3
alexander_vertex_countOption(int) 2
alexander_relationstring not_computed
fk_countint 3
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L9n15_1_c54732ae"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L9n15_1_c54732ae