details/L9n19_1_77e6f49c.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-3/2, 1/2) (1, 1/3) x1^(3/2)x2^(-1/2) q^(3/2) 
{"0": [-1, 1, -1, -1, -1, -1, -1, 1, -1, 1], "1": [1, 1, 1, -1, 1, 1, 1, -1]}
 
(-q^(3/2))*x1^(3/2)*x2^(-1/2) + (q^(-1/2))*x1^(5/2)*x2^(-5/2) + (-q^(-7/2))*x1^(7/2)*x2^(-9/2) + (q^(3/2))*x1^(7/2)*x2^(1/2) + (q^(-15/2))*x1^(9/2)*x2^(-13/2) + (-q^(-5/2))*x1^(9/2)*x2^(-3/2) + (-q^(-25/2))*x1^(11/2)*x2^(-17/2) + (q^(-15/2))*x1^(11/2)*x2^(-7/2) + (-q^(5/2))*x1^(11/2)*x2^(3/2) + (q^(-37/2))*x1^(13/2)*x2^(-21/2) + (-q^(-27/2))*x1^(13/2)*x2^(-11/2) + (q^(-7/2))*x1^(13/2)*x2^(-1/2) + (-q^(-51/2))*x1^(15/2)*x2^(-25/2) + (q^(-41/2))*x1^(15/2)*x2^(-15/2) + (-q^(-21/2))*x1^(15/2)*x2^(-5/2) + (q^(9/2))*x1^(15/2)*x2^(5/2) + (q^(-67/2))*x1^(17/2)*x2^(-29/2) + (-q^(-57/2))*x1^(17/2)*x2^(-19/2) + (q^(-37/2))*x1^(17/2)*x2^(-9/2) + (-q^(-7/2))*x1^(17/2)*x2^(1/2) + (-q^(-85/2))*x1^(19/2)*x2^(-33/2) + (q^(-75/2))*x1^(19/2)*x2^(-23/2) + (-q^(-55/2))*x1^(19/2)*x2^(-13/2) + (q^(-25/2))*x1^(19/2)*x2^(-3/2) + (-q^(15/2))*x1^(19/2)*x2^(7/2)
(-1/2, -3/2) (1, 1) x1^(1/2)x2^(3/2) q^(5/2) 
{"0": [-1, 1, 1, 1, 1, 1, 1, 1, -1, 1], "1": [1, 1, 1, -1, 1, 1, 1, -1]}
 
(-q^(-7/2))*x1^(-7/2)*x2^(19/2) + (q^(-1/2))*x1^(-5/2)*x2^(15/2) + (-q^(3/2))*x1^(-3/2)*x2^(11/2) + (q^(5/2))*x1^(-1/2)*x2^(7/2) + (-q^(15/2))*x1^(-1/2)*x2^(17/2) + (-q^(5/2))*x1^(1/2)*x2^(3/2) + (q^(15/2))*x1^(1/2)*x2^(13/2) + (-q^(13/2))*x1^(3/2)*x2^(9/2) + (q^(33/2))*x1^(3/2)*x2^(19/2) + (q^(9/2))*x1^(5/2)*x2^(5/2) + (-q^(29/2))*x1^(5/2)*x2^(15/2) + (q^(23/2))*x1^(7/2)*x2^(11/2) + (-q^(15/2))*x1^(9/2)*x2^(7/2) + (q^(45/2))*x1^(9/2)*x2^(17/2) + (-q^(35/2))*x1^(11/2)*x2^(13/2) + (q^(23/2))*x1^(13/2)*x2^(9/2) + (-q^(63/2))*x1^(13/2)*x2^(19/2) + (q^(49/2))*x1^(15/2)*x2^(15/2) + (-q^(33/2))*x1^(17/2)*x2^(11/2) + (-q^(65/2))*x1^(19/2)*x2^(17/2)
(-3/2, 1/2) (1, 1/3) x1^(3/2)x2^(-1/2) q^(3/2) 
{"0": [1, 1, -1, -1, -1, -1, -1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1]}
 
(-q^(3/2))*x1^(3/2)*x2^(-1/2) + (q^(-1/2))*x1^(5/2)*x2^(-5/2) + (-q^(-7/2))*x1^(7/2)*x2^(-9/2) + (q^(3/2))*x1^(7/2)*x2^(1/2) + (q^(-15/2))*x1^(9/2)*x2^(-13/2) + (-q^(-5/2))*x1^(9/2)*x2^(-3/2) + (-q^(-25/2))*x1^(11/2)*x2^(-17/2) + (q^(-15/2))*x1^(11/2)*x2^(-7/2) + (-q^(5/2))*x1^(11/2)*x2^(3/2) + (q^(-37/2))*x1^(13/2)*x2^(-21/2) + (-q^(-27/2))*x1^(13/2)*x2^(-11/2) + (q^(-7/2))*x1^(13/2)*x2^(-1/2) + (-q^(-51/2))*x1^(15/2)*x2^(-25/2) + (q^(-41/2))*x1^(15/2)*x2^(-15/2) + (-q^(-21/2))*x1^(15/2)*x2^(-5/2) + (q^(9/2))*x1^(15/2)*x2^(5/2) + (q^(-67/2))*x1^(17/2)*x2^(-29/2) + (-q^(-57/2))*x1^(17/2)*x2^(-19/2) + (q^(-37/2))*x1^(17/2)*x2^(-9/2) + (-q^(-7/2))*x1^(17/2)*x2^(1/2) + (-q^(-85/2))*x1^(19/2)*x2^(-33/2) + (q^(-75/2))*x1^(19/2)*x2^(-23/2) + (-q^(-55/2))*x1^(19/2)*x2^(-13/2) + (q^(-25/2))*x1^(19/2)*x2^(-3/2) + (-q^(15/2))*x1^(19/2)*x2^(7/2)
(-1/2, -3/2) (1, 1) x1^(1/2)x2^(3/2) q^(5/2) 
{"0": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1]}
 
(-q^(-7/2))*x1^(-7/2)*x2^(19/2) + (q^(-1/2))*x1^(-5/2)*x2^(15/2) + (-q^(3/2))*x1^(-3/2)*x2^(11/2) + (q^(5/2))*x1^(-1/2)*x2^(7/2) + (-q^(15/2))*x1^(-1/2)*x2^(17/2) + (-q^(5/2))*x1^(1/2)*x2^(3/2) + (q^(15/2))*x1^(1/2)*x2^(13/2) + (-q^(13/2))*x1^(3/2)*x2^(9/2) + (q^(33/2))*x1^(3/2)*x2^(19/2) + (q^(9/2))*x1^(5/2)*x2^(5/2) + (-q^(29/2))*x1^(5/2)*x2^(15/2) + (q^(23/2))*x1^(7/2)*x2^(11/2) + (-q^(15/2))*x1^(9/2)*x2^(7/2) + (q^(45/2))*x1^(9/2)*x2^(17/2) + (-q^(35/2))*x1^(11/2)*x2^(13/2) + (q^(23/2))*x1^(13/2)*x2^(9/2) + (-q^(63/2))*x1^(13/2)*x2^(19/2) + (q^(49/2))*x1^(15/2)*x2^(15/2) + (-q^(33/2))*x1^(17/2)*x2^(11/2) + (-q^(65/2))*x1^(19/2)*x2^(17/2)
(3/2, -1/2) x1^(-3/2)x2^(1/2) q^(3/2) 
(-q^(3/2))*x1^(-3/2)*x2^(1/2) + (q^(-1/2))*x1^(-5/2)*x2^(5/2) + (-q^(-7/2))*x1^(-7/2)*x2^(9/2) + (q^(3/2))*x1^(-7/2)*x2^(-1/2) + (q^(-15/2))*x1^(-9/2)*x2^(13/2) + (-q^(-5/2))*x1^(-9/2)*x2^(3/2) + (-q^(-25/2))*x1^(-11/2)*x2^(17/2) + (q^(-15/2))*x1^(-11/2)*x2^(7/2) + (-q^(5/2))*x1^(-11/2)*x2^(-3/2) + (q^(-37/2))*x1^(-13/2)*x2^(21/2) + (-q^(-27/2))*x1^(-13/2)*x2^(11/2) + (q^(-7/2))*x1^(-13/2)*x2^(1/2) + (-q^(-51/2))*x1^(-15/2)*x2^(25/2) + (q^(-41/2))*x1^(-15/2)*x2^(15/2) + (-q^(-21/2))*x1^(-15/2)*x2^(5/2) + (q^(9/2))*x1^(-15/2)*x2^(-5/2) + (q^(-67/2))*x1^(-17/2)*x2^(29/2) + (-q^(-57/2))*x1^(-17/2)*x2^(19/2) + (q^(-37/2))*x1^(-17/2)*x2^(9/2) + (-q^(-7/2))*x1^(-17/2)*x2^(-1/2) + (-q^(-85/2))*x1^(-19/2)*x2^(33/2) + (q^(-75/2))*x1^(-19/2)*x2^(23/2) + (-q^(-55/2))*x1^(-19/2)*x2^(13/2) + (q^(-25/2))*x1^(-19/2)*x2^(3/2) + (-q^(15/2))*x1^(-19/2)*x2^(-7/2)
(1/2, 3/2) x1^(-1/2)x2^(-3/2) q^(5/2) 
(-q^(-7/2))*x1^(7/2)*x2^(-19/2) + (q^(-1/2))*x1^(5/2)*x2^(-15/2) + (-q^(3/2))*x1^(3/2)*x2^(-11/2) + (q^(5/2))*x1^(1/2)*x2^(-7/2) + (-q^(15/2))*x1^(1/2)*x2^(-17/2) + (-q^(5/2))*x1^(-1/2)*x2^(-3/2) + (q^(15/2))*x1^(-1/2)*x2^(-13/2) + (-q^(13/2))*x1^(-3/2)*x2^(-9/2) + (q^(33/2))*x1^(-3/2)*x2^(-19/2) + (q^(9/2))*x1^(-5/2)*x2^(-5/2) + (-q^(29/2))*x1^(-5/2)*x2^(-15/2) + (q^(23/2))*x1^(-7/2)*x2^(-11/2) + (-q^(15/2))*x1^(-9/2)*x2^(-7/2) + (q^(45/2))*x1^(-9/2)*x2^(-17/2) + (-q^(35/2))*x1^(-11/2)*x2^(-13/2) + (q^(23/2))*x1^(-13/2)*x2^(-9/2) + (-q^(63/2))*x1^(-13/2)*x2^(-19/2) + (q^(49/2))*x1^(-15/2)*x2^(-15/2) + (-q^(33/2))*x1^(-17/2)*x2^(-11/2) + (-q^(65/2))*x1^(-19/2)*x2^(-17/2)

Braid

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

Multivariable Alexander polynomial

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

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

HFL polytope

Poincaré polynomial
m^(-6)*A1^(-1)*A2^(-2) + m^(-5)*A1^(-1)*A2^(-1) + m^(-5)*A2^(-2) + m^(-4)*A1^(-2) + m^(-4)*A2^(-1) + m^(-3)*A1^(-2)*A2 + m^(-3)*A1^(-1) + m^(-3) + m^(-2)*A1^(-1)*A2 + m^(-2) + m^(-2)*A2 + m^(-2)*A1*A2^(-1) + m^(-1)*A2^2 + m^(-1)*A1 + m^(-1)*A1*A2 + m^(-1)*A1^2*A2^(-1) + A1*A2^2 + A1^2
VertexMaslovRank
(-2, 0)-41
(-1, -2)-61
(0, -2)-51
(2, -1)-11
(2, 0)01
(1, 2)01
(0, 2)-11
(-2, 1)-31
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 180
namestring L9n19{1}
statusstring success
slugstring L9n19_1_77e6f49c
result_filestring details/L9n19_1_77e6f49c.json
complexity_scoreOption(int) 162
strandsOption(int) null
crossingsOption(int) 9
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 18
wall_secondsOption(float) 0.001687
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 17
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 4
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L9n19_1_77e6f49c"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L9n19_1_77e6f49c