details/L11a435_0_1_9df75bad.json

Multivariable Alexander polynomial

ΔL
2*A1^(1/2)*A2^(1/2)*A3^(3/2) - 4*A1^(1/2)*A2^(1/2)*A3^(1/2) + 4*A1^(1/2)*A2^(1/2)*A3^(-1/2) - A1^(1/2)*A2^(1/2)*A3^(-3/2) - 2*A1^(1/2)*A2^(-1/2)*A3^(3/2) + 6*A1^(1/2)*A2^(-1/2)*A3^(1/2) - 6*A1^(1/2)*A2^(-1/2)*A3^(-1/2) + 2*A1^(1/2)*A2^(-1/2)*A3^(-3/2) - 2*A1^(1/2)*A2^(-3/2)*A3^(1/2) + 2*A1^(1/2)*A2^(-3/2)*A3^(-1/2) - A1^(1/2)*A2^(-3/2)*A3^(-3/2) + A1^(-1/2)*A2^(3/2)*A3^(3/2) - 2*A1^(-1/2)*A2^(3/2)*A3^(1/2) + 2*A1^(-1/2)*A2^(3/2)*A3^(-1/2) - 2*A1^(-1/2)*A2^(1/2)*A3^(3/2) + 6*A1^(-1/2)*A2^(1/2)*A3^(1/2) - 6*A1^(-1/2)*A2^(1/2)*A3^(-1/2) + 2*A1^(-1/2)*A2^(1/2)*A3^(-3/2) + A1^(-1/2)*A2^(-1/2)*A3^(3/2) - 4*A1^(-1/2)*A2^(-1/2)*A3^(1/2) + 4*A1^(-1/2)*A2^(-1/2)*A3^(-1/2) - 2*A1^(-1/2)*A2^(-1/2)*A3^(-3/2)

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

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Dual Thurston polytope

VertexDual to fibered face
(1, 1, -3) yes
(1, -3, 1) no
(1, -3, -3) yes
(-1, 3, -1) no
(1, 1, 3) no
(-1, 1, -3) no
(1, -1, 3) no
(-1, 3, 3) yes
(-1, -1, 3) yes
(-1, -1, -3) no
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HFL polytope

Poincaré polynomial
2*m^(-4)*A1^(-1)*A2^(-1)*A3^(-2) + m^(-4)*A2^(-2)*A3^(-2) + 6*m^(-3)*A1^(-1)*A2^(-1)*A3^(-1) + 4*m^(-3)*A1^(-1)*A3^(-2) + 3*m^(-3)*A2^(-2)*A3^(-1) + 5*m^(-3)*A2^(-1)*A3^(-2) + m^(-3)*A1*A2^(-2)*A3^(-2) + 8*m^(-2)*A1^(-1)*A2^(-1) + 14*m^(-2)*A1^(-1)*A3^(-1) + 2*m^(-2)*A1^(-1)*A2*A3^(-2) + 4*m^(-2)*A2^(-2) + 17*m^(-2)*A2^(-1)*A3^(-1) + 7*m^(-2)*A3^(-2) + 3*m^(-2)*A1*A2^(-2)*A3^(-1) + 3*m^(-2)*A1*A2^(-1)*A3^(-2) + 5*m^(-1)*A1^(-1)*A2^(-1)*A3 + 20*m^(-1)*A1^(-1) + 10*m^(-1)*A1^(-1)*A2*A3^(-1) + 2*m^(-1)*A2^(-2)*A3 + 24*m^(-1)*A2^(-1) + 27*m^(-1)*A3^(-1) + 3*m^(-1)*A2*A3^(-2) + 4*m^(-1)*A1*A2^(-2) + 11*m^(-1)*A1*A2^(-1)*A3^(-1) + 3*m^(-1)*A1*A3^(-2) + A1^(-1)*A2^(-1)*A3^2 + 13*A1^(-1)*A3 + 16*A1^(-1)*A2 + 2*A1^(-1)*A2^2*A3^(-1) + 15*A2^(-1)*A3 + 40 + 15*A2*A3^(-1) + 2*A1*A2^(-2)*A3 + 16*A1*A2^(-1) + 13*A1*A3^(-1) + A1*A2*A3^(-2) + 3*m*A1^(-1)*A3^2 + 11*m*A1^(-1)*A2*A3 + 4*m*A1^(-1)*A2^2 + 3*m*A2^(-1)*A3^2 + 27*m*A3 + 24*m*A2 + 2*m*A2^2*A3^(-1) + 10*m*A1*A2^(-1)*A3 + 20*m*A1 + 5*m*A1*A2*A3^(-1) + 3*m^2*A1^(-1)*A2*A3^2 + 3*m^2*A1^(-1)*A2^2*A3 + 7*m^2*A3^2 + 17*m^2*A2*A3 + 4*m^2*A2^2 + 2*m^2*A1*A2^(-1)*A3^2 + 14*m^2*A1*A3 + 8*m^2*A1*A2 + m^3*A1^(-1)*A2^2*A3^2 + 5*m^3*A2*A3^2 + 3*m^3*A2^2*A3 + 4*m^3*A1*A3^2 + 6*m^3*A1*A2*A3 + m^4*A2^2*A3^2 + 2*m^4*A1*A2*A3^2
VertexMaslovRank
(-1, -1, -2)-42
(-1, -1, 2)01
(-1, 1, -2)-22
(-1, 2, -1)02
(-1, 2, 2)31
(0, -2, -2)-41
(0, -2, 1)-12
(0, 2, -1)12
(0, 2, 2)41
(1, -2, -2)-31
(1, -2, 1)02
(1, -1, 2)22
(1, 1, -2)01
(1, 1, 2)42
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Record

FL/HFL Links

orderOption(int) 2498
namestring L11a435{0;1}
statusstring success
slugstring L11a435_0_1_9df75bad
result_filestring details/L11a435_0_1_9df75bad.json
complexity_scoreOption(int) 363
strandsOption(int) null
crossingsOption(int) 11
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 512
wall_secondsOption(float) 0.005992
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 61
vertex_countOption(int) 14
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 22
alexander_vertex_countOption(int) 10
alexander_relationstring not_computed
fk_countint 0
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L11a435_0_1_9df75bad"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L11a435_0_1_9df75bad