details/L8a14_1_2f57863d.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(3/2, -3/2) (1/2, 1) x1^(-3/2)x2^(3/2) 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, 1, 1]}
 
(-q^(43/2))*x1^(-19/2)*x2^(19/2) + (q^(19/2))*x1^(-13/2)*x2^(13/2) + (-q^(13/2))*x1^(-11/2)*x2^(11/2) + (q^(1/2))*x1^(-5/2)*x2^(5/2) + (-q^(-1/2))*x1^(-3/2)*x2^(3/2)
(3/2, -3/2) (1/2, 1) x1^(-3/2)x2^(3/2) 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, 1, 1]}
 
(-q^(43/2))*x1^(-19/2)*x2^(19/2) + (q^(19/2))*x1^(-13/2)*x2^(13/2) + (-q^(13/2))*x1^(-11/2)*x2^(11/2) + (q^(1/2))*x1^(-5/2)*x2^(5/2) + (-q^(-1/2))*x1^(-3/2)*x2^(3/2)
(-3/2, 3/2) x1^(3/2)x2^(-3/2) q^(-1/2) 
(-q^(43/2))*x1^(19/2)*x2^(-19/2) + (q^(19/2))*x1^(13/2)*x2^(-13/2) + (-q^(13/2))*x1^(11/2)*x2^(-11/2) + (q^(1/2))*x1^(5/2)*x2^(-5/2) + (-q^(-1/2))*x1^(3/2)*x2^(-3/2)

Braid

Braid word Components Crossings Strands
[1, -2, -1, -1, -3, -4, 3, -4, -3, -2, 3] 2 11 5

Multivariable Alexander polynomial

ΔL
A1^(3/2)*A2^(-3/2) + A1^(1/2)*A2^(-1/2) + A1^(-1/2)*A2^(1/2) + A1^(-3/2)*A2^(3/2)

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-202-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-3, 3) yes
(3, -3) yes
Dual Thurston polygon0505h1h2

HFL polytope

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

Record

FL/HFL Links

orderOption(int) 50
namestring L8a14{1}
statusstring success
slugstring L8a14_1_2f57863d
result_filestring details/L8a14_1_2f57863d.json
complexity_scoreOption(int) 128
strandsOption(int) null
crossingsOption(int) 8
component_countOption(int) 2
girthOption(int) 4
total_rankOption(int) 16
wall_secondsOption(float) 0.001363
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) 2
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L8a14_1_2f57863d"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L8a14_1_2f57863d