details/L10n10_1_c05183fa.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1/2, -5/2) (1, 1) x1^(-1/2)x2^(5/2) 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]}
 
(-2*q^(-9/2))*x1^(-3/2)*x2^(13/2) + (-q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(15/2) + (-2*q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-3/2)*x2^(17/2) + (-q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 11*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-3/2)*x2^(19/2) + (-q^(-1/2))*x1^(-1/2)*x2^(5/2) + (-2*q^(-1/2))*x1^(-1/2)*x2^(7/2) + (-q^(1/2) - 3*q^(-1/2))*x1^(-1/2)*x2^(9/2) + (-2*q^(3/2) - 2*q^(1/2) - 4*q^(-1/2))*x1^(-1/2)*x2^(11/2) + (-q^(7/2) - 3*q^(5/2) - 4*q^(3/2) - 3*q^(1/2) - 5*q^(-1/2))*x1^(-1/2)*x2^(13/2) + (-2*q^(11/2) - 2*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 6*q^(3/2) - 4*q^(1/2) - 6*q^(-1/2))*x1^(-1/2)*x2^(15/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 7*q^(11/2) - 9*q^(9/2) - 11*q^(7/2) - 9*q^(5/2) - 8*q^(3/2) - 5*q^(1/2) - 7*q^(-1/2))*x1^(-1/2)*x2^(17/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 8*q^(17/2) - 12*q^(15/2) - 12*q^(13/2) - 18*q^(11/2) - 16*q^(9/2) - 16*q^(7/2) - 12*q^(5/2) - 10*q^(3/2) - 6*q^(1/2) - 8*q^(-1/2))*x1^(-1/2)*x2^(19/2)
(1/2, -5/2) (1, 1) x1^(-1/2)x2^(5/2) 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]}
 
(-2*q^(-9/2))*x1^(-3/2)*x2^(13/2) + (-q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(15/2) + (-2*q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-3/2)*x2^(17/2) + (-q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 11*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-3/2)*x2^(19/2) + (-q^(-1/2))*x1^(-1/2)*x2^(5/2) + (-2*q^(-1/2))*x1^(-1/2)*x2^(7/2) + (-q^(1/2) - 3*q^(-1/2))*x1^(-1/2)*x2^(9/2) + (-2*q^(3/2) - 2*q^(1/2) - 4*q^(-1/2))*x1^(-1/2)*x2^(11/2) + (-q^(7/2) - 3*q^(5/2) - 4*q^(3/2) - 3*q^(1/2) - 5*q^(-1/2))*x1^(-1/2)*x2^(13/2) + (-2*q^(11/2) - 2*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 6*q^(3/2) - 4*q^(1/2) - 6*q^(-1/2))*x1^(-1/2)*x2^(15/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 7*q^(11/2) - 9*q^(9/2) - 11*q^(7/2) - 9*q^(5/2) - 8*q^(3/2) - 5*q^(1/2) - 7*q^(-1/2))*x1^(-1/2)*x2^(17/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 8*q^(17/2) - 12*q^(15/2) - 12*q^(13/2) - 18*q^(11/2) - 16*q^(9/2) - 16*q^(7/2) - 12*q^(5/2) - 10*q^(3/2) - 6*q^(1/2) - 8*q^(-1/2))*x1^(-1/2)*x2^(19/2)
(-1/2, 5/2) x1^(1/2)x2^(-5/2) q^(-1/2) 
(-2*q^(-9/2))*x1^(3/2)*x2^(-13/2) + (-q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(3/2)*x2^(-15/2) + (-2*q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(3/2)*x2^(-17/2) + (-q^(-1/2) - 4*q^(-3/2) - 8*q^(-5/2) - 11*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(3/2)*x2^(-19/2) + (-q^(-1/2))*x1^(1/2)*x2^(-5/2) + (-2*q^(-1/2))*x1^(1/2)*x2^(-7/2) + (-q^(1/2) - 3*q^(-1/2))*x1^(1/2)*x2^(-9/2) + (-2*q^(3/2) - 2*q^(1/2) - 4*q^(-1/2))*x1^(1/2)*x2^(-11/2) + (-q^(7/2) - 3*q^(5/2) - 4*q^(3/2) - 3*q^(1/2) - 5*q^(-1/2))*x1^(1/2)*x2^(-13/2) + (-2*q^(11/2) - 2*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 6*q^(3/2) - 4*q^(1/2) - 6*q^(-1/2))*x1^(1/2)*x2^(-15/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 7*q^(11/2) - 9*q^(9/2) - 11*q^(7/2) - 9*q^(5/2) - 8*q^(3/2) - 5*q^(1/2) - 7*q^(-1/2))*x1^(1/2)*x2^(-17/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 8*q^(17/2) - 12*q^(15/2) - 12*q^(13/2) - 18*q^(11/2) - 16*q^(9/2) - 16*q^(7/2) - 12*q^(5/2) - 10*q^(3/2) - 6*q^(1/2) - 8*q^(-1/2))*x1^(1/2)*x2^(-19/2)

Braid

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

Multivariable Alexander polynomial

ΔL
2*A1^(1/2)*A2^(-3/2) - A1^(1/2)*A2^(-5/2) - A1^(-1/2)*A2^(5/2) + 2*A1^(-1/2)*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-0.500.5-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(1, -5) yes
(1, -3) no
(-1, 5) yes
(-1, 3) no
Dual Thurston polygon-101-505h1h2

HFL polytope

Poincaré polynomial
m^(-3)*A2^(-3) + 3*m^(-2)*A2^(-2) + m^(-2)*A2^(-1) + m^(-2)*A1*A2^(-3) + 3*m^(-1)*A2^(-1) + 3*m^(-1) + 3*m^(-1)*A1*A2^(-2) + 2*A1^(-1)*A2 + 3 + A2 + 2*A1*A2^(-1) + 3*m*A1^(-1)*A2^2 + 3*m*A2 + m^2*A1^(-1)*A2^3 + 3*m^2*A2^2 + m^3*A2^3
VertexMaslovRank
(-1, 1)02
(0, -3)-31
(1, -3)-21
(1, -1)02
(0, 3)31
(-1, 3)21
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 482
namestring L10n10{1}
statusstring success
slugstring L10n10_1_c05183fa
result_filestring details/L10n10_1_c05183fa.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 34
wall_secondsOption(float) 0.001659
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) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10n10_1_c05183fa"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n10_1_c05183fa