details/L11n77_1_0726d9d7.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^(-29/2)
{"0": [1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1], "1": [1, 1, 1, 1, 1, 1]}
(-q^(1/2))*x1^(-1/2)*x2^(5/2) + (-4*q^(1/2))*x1^(-1/2)*x2^(7/2) + (-3*q^(-3/2))*x1^(-3/2)*x2^(9/2) + (-2*q^(3/2) - 10*q^(1/2) + 3*q^(-1/2))*x1^(-1/2)*x2^(9/2) + (-4*q^(-1/2) - 12*q^(-3/2) - q^(-5/2))*x1^(-3/2)*x2^(11/2) + (-4*q^(5/2) - 8*q^(3/2) - 16*q^(1/2) + 12*q^(-1/2) + 5*q^(-3/2))*x1^(-1/2)*x2^(11/2) + (-q^(-7/2) - 3*q^(-9/2) - 5*q^(-11/2))*x1^(-5/2)*x2^(13/2) + (-9*q^(1/2) - 22*q^(-1/2) - 33*q^(-3/2) + 3*q^(-5/2) + 9*q^(-7/2) + 2*q^(-9/2))*x1^(-3/2)*x2^(13/2) + (-2*q^(9/2) - 6*q^(7/2) - 17*q^(5/2) - 11*q^(3/2) - 13*q^(1/2) + 37*q^(-1/2) + 17*q^(-3/2) + 2*q^(-5/2))*x1^(-1/2)*x2^(13/2) + (-4*q^(-5/2) - 16*q^(-7/2) - 22*q^(-9/2) - 21*q^(-11/2) - q^(-13/2) - 2*q^(-15/2))*x1^(-5/2)*x2^(15/2) + (-4*q^(5/2) - 20*q^(3/2) - 52*q^(1/2) - 70*q^(-1/2) - 54*q^(-3/2) + 41*q^(-5/2) + 55*q^(-7/2) + 24*q^(-9/2) + 3*q^(-11/2) + 2*q^(-13/2))*x1^(-3/2)*x2^(15/2) + (-4*q^(13/2) - 4*q^(11/2) - 16*q^(9/2) - 24*q^(7/2) - 24*q^(5/2) + 12*q^(3/2) + 23*q^(1/2) + 86*q^(-1/2) + 39*q^(-3/2) - 3*q^(-7/2) - 7*q^(-9/2))*x1^(-1/2)*x2^(15/2) + (-3*q^(-15/2) - 4*q^(-17/2) - 8*q^(-19/2) - 5*q^(-21/2) - 7*q^(-23/2))*x1^(-7/2)*x2^(17/2) + (-2*q^(-1/2) - 18*q^(-3/2) - 49*q^(-5/2) - 91*q^(-7/2) - 88*q^(-9/2) - 53*q^(-11/2) + 22*q^(-13/2) + 19*q^(-15/2) + 12*q^(-17/2) + 2*q^(-19/2) + 2*q^(-21/2))*x1^(-5/2)*x2^(17/2) + (-8*q^(9/2) - 18*q^(7/2) - 58*q^(5/2) - 116*q^(3/2) - 161*q^(1/2) - 112*q^(-1/2) + 12*q^(-3/2) + 214*q^(-5/2) + 213*q^(-7/2) + 97*q^(-9/2) + 16*q^(-11/2) - 11*q^(-13/2) - 3*q^(-15/2))*x1^(-3/2)*x2^(17/2) + (-2*q^(19/2) - 6*q^(17/2) - 8*q^(15/2) - 22*q^(13/2) - 20*q^(11/2) - 44*q^(9/2) - 18*q^(7/2) + 30*q^(5/2) + 113*q^(3/2) + 111*q^(1/2) + 159*q^(-1/2) + 49*q^(-3/2) - 30*q^(-5/2) - 31*q^(-7/2) - 33*q^(-9/2) - 9*q^(-11/2) - 9*q^(-13/2))*x1^(-1/2)*x2^(17/2) + (-4*q^(-11/2) - 16*q^(-13/2) - 36*q^(-15/2) - 53*q^(-17/2) - 58*q^(-19/2) - 37*q^(-21/2) - 30*q^(-23/2) - 3*q^(-25/2) - 4*q^(-27/2) - 2*q^(-29/2))*x1^(-7/2)*x2^(19/2) + (-4*q^(3/2) - 24*q^(1/2) - 68*q^(-1/2) - 168*q^(-3/2) - 268*q^(-5/2) - 321*q^(-7/2) - 205*q^(-9/2) - 6*q^(-11/2) + 214*q^(-13/2) + 203*q^(-15/2) + 114*q^(-17/2) + 29*q^(-19/2) + 11*q^(-21/2) + 6*q^(-23/2) + 4*q^(-25/2) + 2*q^(-27/2))*x1^(-5/2)*x2^(19/2) + (-4*q^(15/2) - 16*q^(13/2) - 36*q^(11/2) - 84*q^(9/2) - 156*q^(7/2) - 268*q^(5/2) - 318*q^(3/2) - 212*q^(1/2) + 107*q^(-1/2) + 464*q^(-3/2) + 761*q^(-5/2) + 599*q^(-7/2) + 225*q^(-9/2) - 31*q^(-11/2) - 114*q^(-13/2) - 81*q^(-15/2) - 35*q^(-17/2) - 10*q^(-19/2) - 4*q^(-21/2) - 2*q^(-23/2))*x1^(-3/2)*x2^(19/2) + (-4*q^(25/2) - 4*q^(23/2) - 12*q^(21/2) - 20*q^(19/2) - 32*q^(17/2) - 28*q^(15/2) - 48*q^(13/2) - 24*q^(11/2) + 4*q^(9/2) + 130*q^(7/2) + 246*q^(5/2) + 320*q^(3/2) + 227*q^(1/2) + 179*q^(-1/2) - 34*q^(-3/2) - 166*q^(-5/2) - 137*q^(-7/2) - 117*q^(-9/2) - 44*q^(-11/2) - 35*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(-1/2)*x2^(19/2)
(-1/2, 5/2) x1^(1/2)x2^(-5/2) q^(-29/2)
(-q^(1/2))*x1^(1/2)*x2^(-5/2) + (-4*q^(1/2))*x1^(1/2)*x2^(-7/2) + (-3*q^(-3/2))*x1^(3/2)*x2^(-9/2) + (-2*q^(3/2) - 10*q^(1/2) + 3*q^(-1/2))*x1^(1/2)*x2^(-9/2) + (-4*q^(-1/2) - 12*q^(-3/2) - q^(-5/2))*x1^(3/2)*x2^(-11/2) + (-4*q^(5/2) - 8*q^(3/2) - 16*q^(1/2) + 12*q^(-1/2) + 5*q^(-3/2))*x1^(1/2)*x2^(-11/2) + (-q^(-7/2) - 3*q^(-9/2) - 5*q^(-11/2))*x1^(5/2)*x2^(-13/2) + (-9*q^(1/2) - 22*q^(-1/2) - 33*q^(-3/2) + 3*q^(-5/2) + 9*q^(-7/2) + 2*q^(-9/2))*x1^(3/2)*x2^(-13/2) + (-2*q^(9/2) - 6*q^(7/2) - 17*q^(5/2) - 11*q^(3/2) - 13*q^(1/2) + 37*q^(-1/2) + 17*q^(-3/2) + 2*q^(-5/2))*x1^(1/2)*x2^(-13/2) + (-4*q^(-5/2) - 16*q^(-7/2) - 22*q^(-9/2) - 21*q^(-11/2) - q^(-13/2) - 2*q^(-15/2))*x1^(5/2)*x2^(-15/2) + (-4*q^(5/2) - 20*q^(3/2) - 52*q^(1/2) - 70*q^(-1/2) - 54*q^(-3/2) + 41*q^(-5/2) + 55*q^(-7/2) + 24*q^(-9/2) + 3*q^(-11/2) + 2*q^(-13/2))*x1^(3/2)*x2^(-15/2) + (-4*q^(13/2) - 4*q^(11/2) - 16*q^(9/2) - 24*q^(7/2) - 24*q^(5/2) + 12*q^(3/2) + 23*q^(1/2) + 86*q^(-1/2) + 39*q^(-3/2) - 3*q^(-7/2) - 7*q^(-9/2))*x1^(1/2)*x2^(-15/2) + (-3*q^(-15/2) - 4*q^(-17/2) - 8*q^(-19/2) - 5*q^(-21/2) - 7*q^(-23/2))*x1^(7/2)*x2^(-17/2) + (-2*q^(-1/2) - 18*q^(-3/2) - 49*q^(-5/2) - 91*q^(-7/2) - 88*q^(-9/2) - 53*q^(-11/2) + 22*q^(-13/2) + 19*q^(-15/2) + 12*q^(-17/2) + 2*q^(-19/2) + 2*q^(-21/2))*x1^(5/2)*x2^(-17/2) + (-8*q^(9/2) - 18*q^(7/2) - 58*q^(5/2) - 116*q^(3/2) - 161*q^(1/2) - 112*q^(-1/2) + 12*q^(-3/2) + 214*q^(-5/2) + 213*q^(-7/2) + 97*q^(-9/2) + 16*q^(-11/2) - 11*q^(-13/2) - 3*q^(-15/2))*x1^(3/2)*x2^(-17/2) + (-2*q^(19/2) - 6*q^(17/2) - 8*q^(15/2) - 22*q^(13/2) - 20*q^(11/2) - 44*q^(9/2) - 18*q^(7/2) + 30*q^(5/2) + 113*q^(3/2) + 111*q^(1/2) + 159*q^(-1/2) + 49*q^(-3/2) - 30*q^(-5/2) - 31*q^(-7/2) - 33*q^(-9/2) - 9*q^(-11/2) - 9*q^(-13/2))*x1^(1/2)*x2^(-17/2) + (-4*q^(-11/2) - 16*q^(-13/2) - 36*q^(-15/2) - 53*q^(-17/2) - 58*q^(-19/2) - 37*q^(-21/2) - 30*q^(-23/2) - 3*q^(-25/2) - 4*q^(-27/2) - 2*q^(-29/2))*x1^(7/2)*x2^(-19/2) + (-4*q^(3/2) - 24*q^(1/2) - 68*q^(-1/2) - 168*q^(-3/2) - 268*q^(-5/2) - 321*q^(-7/2) - 205*q^(-9/2) - 6*q^(-11/2) + 214*q^(-13/2) + 203*q^(-15/2) + 114*q^(-17/2) + 29*q^(-19/2) + 11*q^(-21/2) + 6*q^(-23/2) + 4*q^(-25/2) + 2*q^(-27/2))*x1^(5/2)*x2^(-19/2) + (-4*q^(15/2) - 16*q^(13/2) - 36*q^(11/2) - 84*q^(9/2) - 156*q^(7/2) - 268*q^(5/2) - 318*q^(3/2) - 212*q^(1/2) + 107*q^(-1/2) + 464*q^(-3/2) + 761*q^(-5/2) + 599*q^(-7/2) + 225*q^(-9/2) - 31*q^(-11/2) - 114*q^(-13/2) - 81*q^(-15/2) - 35*q^(-17/2) - 10*q^(-19/2) - 4*q^(-21/2) - 2*q^(-23/2))*x1^(3/2)*x2^(-19/2) + (-4*q^(25/2) - 4*q^(23/2) - 12*q^(21/2) - 20*q^(19/2) - 32*q^(17/2) - 28*q^(15/2) - 48*q^(13/2) - 24*q^(11/2) + 4*q^(9/2) + 130*q^(7/2) + 246*q^(5/2) + 320*q^(3/2) + 227*q^(1/2) + 179*q^(-1/2) - 34*q^(-3/2) - 166*q^(-5/2) - 137*q^(-7/2) - 117*q^(-9/2) - 44*q^(-11/2) - 35*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(1/2)*x2^(-19/2)

Braid

Braid word Components Crossings Strands
[1, -2, 3, -2, -4, 1, 3, 2, 2, 3, 4, 3, -2] 2 13 5

Multivariable Alexander polynomial

ΔL
-3*A1^(1/2)*A2^(1/2) + 7*A1^(1/2)*A2^(-1/2) - 4*A1^(1/2)*A2^(-3/2) + A1^(1/2)*A2^(-5/2) + A1^(-1/2)*A2^(5/2) - 4*A1^(-1/2)*A2^(3/2) + 7*A1^(-1/2)*A2^(1/2) - 3*A1^(-1/2)*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-0.500.5-202A1A2

Dual Thurston polytope

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

HFL polytope

Poincaré polynomial
m^(-4)*A2^(-3) + 3*m^(-3)*A1^(-1)*A2^(-1) + 5*m^(-3)*A2^(-2) + m^(-3)*A1*A2^(-3) + 10*m^(-2)*A1^(-1) + 14*m^(-2)*A2^(-1) + 5*m^(-2)*A1*A2^(-2) + 11*m^(-1)*A1^(-1)*A2 + 20*m^(-1) + 11*m^(-1)*A1*A2^(-1) + 5*A1^(-1)*A2^2 + 14*A2 + 10*A1 + m*A1^(-1)*A2^3 + 5*m*A2^2 + 3*m*A1*A2 + m^2*A2^3
VertexMaslovRank
(-1, -1)-33
(0, -3)-41
(1, -3)-31
(1, 1)13
(0, 3)21
(-1, 3)11
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 1834
namestring L11n77{1}
statusstring success
slugstring L11n77_1_0726d9d7
result_filestring details/L11n77_1_0726d9d7.json
complexity_scoreOption(int) 242
strandsOption(int) null
crossingsOption(int) 11
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 120
wall_secondsOption(float) 0.002584
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 17
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 8
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 1
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L11n77_1_0726d9d7"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L11n77_1_0726d9d7