details/L6a3_0_1af3b64c.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1, -1) (1, 1) x1^(1)x2^(1) q^(-5/2) 
{"0": [-1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1]}
 
(-q^(-5/2))*x1*x2 + (q^(-7/2))*x1^(2)*x2^(2) + (-q^(-15/2))*x1^(4)*x2^(4) + (q^(-21/2))*x1^(5)*x2^(5) + (-q^(-37/2))*x1^(7)*x2^(7) + (q^(-47/2))*x1^(8)*x2^(8)
(-1, -1) (1, 1) x1^(1)x2^(1) q^(-5/2) 
{"0": [1, -1, 1, -1, 1, -1], "1": [-1, 1, -1, 1, -1, 1]}
 
(-q^(-5/2))*x1*x2 + (q^(-7/2))*x1^(2)*x2^(2) + (-q^(-15/2))*x1^(4)*x2^(4) + (q^(-21/2))*x1^(5)*x2^(5) + (-q^(-37/2))*x1^(7)*x2^(7) + (q^(-47/2))*x1^(8)*x2^(8)
(1, 1) x1^(-1)x2^(-1) q^(-5/2) 
(-q^(-5/2))*x1^(-1)*x2^(-1) + (q^(-7/2))*x1^(-2)*x2^(-2) + (-q^(-15/2))*x1^(-4)*x2^(-4) + (q^(-21/2))*x1^(-5)*x2^(-5) + (-q^(-37/2))*x1^(-7)*x2^(-7) + (q^(-47/2))*x1^(-8)*x2^(-8)

Braid

Braid word Components Crossings Strands
[-1, -1, -1, -1, -1, -1] 2 6 2

Multivariable Alexander polynomial

ΔL
-A1*A2 - 1 - A1^(-1)*A2^(-1)

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-101-101A1A2

Dual Thurston polytope

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

HFL polytope

Poincaré polynomial
m^(-1)*A1^(-3/2)*A2^(-3/2) + A1^(-3/2)*A2^(-1/2) + A1^(-1/2)*A2^(-3/2) + 2*m*A1^(-1/2)*A2^(-1/2) + m^2*A1^(-1/2)*A2^(1/2) + m^2*A1^(1/2)*A2^(-1/2) + 2*m^3*A1^(1/2)*A2^(1/2) + m^4*A1^(1/2)*A2^(3/2) + m^4*A1^(3/2)*A2^(1/2) + m^5*A1^(3/2)*A2^(3/2)
VertexMaslovRank
(-3/2, -3/2)-11
(-1/2, -3/2)01
(3/2, 1/2)41
(3/2, 3/2)51
(1/2, 3/2)41
(-3/2, -1/2)01
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 11
namestring L6a3{0}
statusstring success
slugstring L6a3_0_1af3b64c
result_filestring details/L6a3_0_1af3b64c.json
complexity_scoreOption(int) 72
strandsOption(int) null
crossingsOption(int) 6
component_countOption(int) 2
girthOption(int) 4
total_rankOption(int) 12
wall_secondsOption(float) 0.001244
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 10
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 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L6a3_0_1af3b64c"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L6a3_0_1af3b64c