details/L9n18_0_72e25043.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-3/2, -3/2) (1, 1) x1^(3/2)x2^(3/2) q^(-7/2) 
{"0": [-1, -1, -1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(-7/2))*x1^(3/2)*x2^(3/2) + (q^(-11/2))*x1^(5/2)*x2^(7/2) + (q^(-11/2))*x1^(7/2)*x2^(5/2) + (-q^(-17/2))*x1^(7/2)*x2^(11/2) + (-q^(-19/2))*x1^(9/2)*x2^(9/2) + (q^(-25/2))*x1^(9/2)*x2^(15/2) + (-q^(-17/2))*x1^(11/2)*x2^(7/2) + (q^(-29/2))*x1^(11/2)*x2^(13/2) + (-q^(-35/2))*x1^(11/2)*x2^(19/2) + (q^(-29/2))*x1^(13/2)*x2^(11/2) + (-q^(-41/2))*x1^(13/2)*x2^(17/2) + (q^(-25/2))*x1^(15/2)*x2^(9/2) + (-q^(-43/2))*x1^(15/2)*x2^(15/2) + (-q^(-41/2))*x1^(17/2)*x2^(13/2) + (q^(-59/2))*x1^(17/2)*x2^(19/2) + (-q^(-35/2))*x1^(19/2)*x2^(11/2) + (q^(-59/2))*x1^(19/2)*x2^(17/2)
(-3/2, -3/2) (1, 1) x1^(3/2)x2^(3/2) q^(-7/2) 
{"0": [1, -1, -1, -1, -1, -1, -1, -1], "1": [-1, 1, -1, -1, -1, -1, -1, -1, -1, 1]}
 
(-q^(-7/2))*x1^(3/2)*x2^(3/2) + (q^(-11/2))*x1^(5/2)*x2^(7/2) + (q^(-11/2))*x1^(7/2)*x2^(5/2) + (-q^(-17/2))*x1^(7/2)*x2^(11/2) + (-q^(-19/2))*x1^(9/2)*x2^(9/2) + (q^(-25/2))*x1^(9/2)*x2^(15/2) + (-q^(-17/2))*x1^(11/2)*x2^(7/2) + (q^(-29/2))*x1^(11/2)*x2^(13/2) + (-q^(-35/2))*x1^(11/2)*x2^(19/2) + (q^(-29/2))*x1^(13/2)*x2^(11/2) + (-q^(-41/2))*x1^(13/2)*x2^(17/2) + (q^(-25/2))*x1^(15/2)*x2^(9/2) + (-q^(-43/2))*x1^(15/2)*x2^(15/2) + (-q^(-41/2))*x1^(17/2)*x2^(13/2) + (q^(-59/2))*x1^(17/2)*x2^(19/2) + (-q^(-35/2))*x1^(19/2)*x2^(11/2) + (q^(-59/2))*x1^(19/2)*x2^(17/2)
(3/2, 3/2) x1^(-3/2)x2^(-3/2) q^(-7/2) 
(-q^(-7/2))*x1^(-3/2)*x2^(-3/2) + (q^(-11/2))*x1^(-5/2)*x2^(-7/2) + (q^(-11/2))*x1^(-7/2)*x2^(-5/2) + (-q^(-17/2))*x1^(-7/2)*x2^(-11/2) + (-q^(-19/2))*x1^(-9/2)*x2^(-9/2) + (q^(-25/2))*x1^(-9/2)*x2^(-15/2) + (-q^(-17/2))*x1^(-11/2)*x2^(-7/2) + (q^(-29/2))*x1^(-11/2)*x2^(-13/2) + (-q^(-35/2))*x1^(-11/2)*x2^(-19/2) + (q^(-29/2))*x1^(-13/2)*x2^(-11/2) + (-q^(-41/2))*x1^(-13/2)*x2^(-17/2) + (q^(-25/2))*x1^(-15/2)*x2^(-9/2) + (-q^(-43/2))*x1^(-15/2)*x2^(-15/2) + (-q^(-41/2))*x1^(-17/2)*x2^(-13/2) + (q^(-59/2))*x1^(-17/2)*x2^(-19/2) + (-q^(-35/2))*x1^(-19/2)*x2^(-11/2) + (q^(-59/2))*x1^(-19/2)*x2^(-17/2)

Braid

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

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
(1, -1) yes
(3, 3) yes
(-1, 1) yes
Dual Thurston polygon0505h1h2

HFL polytope

Poincaré polynomial
m^(-1)*A1^(-2)*A2^(-2) + A1^(-2)*A2^(-1) + A1^(-1)*A2^(-2) + m*A1^(-1)*A2^(-1) + m*A1^(-1) + m*A2^(-1) + m^2*A1^(-1)*A2 + 2*m^2 + m^2*A1*A2^(-1) + m^3*A2 + m^3*A1 + m^5*A1*A2 + m^6*A1*A2^2 + m^6*A1^2*A2 + m^7*A1^2*A2^2
VertexMaslovRank
(-2, -2)-11
(-1, -2)01
(1, -1)21
(2, 1)61
(2, 2)71
(1, 2)61
(-1, 1)21
(-2, -1)01
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 177
namestring L9n18{0}
statusstring success
slugstring L9n18_0_72e25043
result_filestring details/L9n18_0_72e25043.json
complexity_scoreOption(int) 162
strandsOption(int) null
crossingsOption(int) 9
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 16
wall_secondsOption(float) 0.001617
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 15
vertex_countOption(int) 8
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 4
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L9n18_0_72e25043"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L9n18_0_72e25043