details/L10n77_0_0_4fab5bbe.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, -3/2, -3/2) (1, 1, 1) x1^(1/2)x2^(3/2)x3^(3/2) q^(-4) 
{"0": [-1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, -1], "2": [-1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(-4))*x1^(1/2)*x2^(3/2)*x3^(3/2) + (-q^(-10))*x1^(3/2)*x2^(9/2)*x3^(9/2)
(-1/2, -3/2, -3/2) (1, 1, 1) x1^(1/2)x2^(3/2)x3^(3/2) q^(-4) 
{"0": [1, -1, -1, -1], "1": [-1, 1, -1, -1, -1, -1, -1, -1], "2": [-1, -1, 1, -1, -1, -1, -1, -1]}
 
(-q^(-4))*x1^(1/2)*x2^(3/2)*x3^(3/2) + (-q^(-10))*x1^(3/2)*x2^(9/2)*x3^(9/2)
(1/2, 3/2, 3/2) x1^(-1/2)x2^(-3/2)x3^(-3/2) q^(-4) 
(-q^(-4))*x1^(-1/2)*x2^(-3/2)*x3^(-3/2) + (-q^(-10))*x1^(-3/2)*x2^(-9/2)*x3^(-9/2)

Braid

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

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(3/2)*A3^(3/2) - A1^(-1/2)*A2^(-3/2)*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, 3, 3) yes
(-1, -3, -3) yes
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HFL polytope

Poincaré polynomial
m^(-2)*A1^(-1)*A2^(-2)*A3^(-2) + m^(-1)*A1^(-1)*A2^(-2)*A3^(-1) + m^(-1)*A1^(-1)*A2^(-1)*A3^(-2) + m^(-1)*A2^(-2)*A3^(-2) + A1^(-1)*A2^(-1)*A3^(-1) + A2^(-2)*A3^(-1) + A2^(-1)*A3^(-2) + A2^(-1)*A3^(-1) + 2*m*A2^(-1)*A3^(-1) + m*A2^(-1) + m*A3^(-1) + m^2*A2^(-1) + m^2*A3^(-1) + 2*m^2 + 2*m^3 + m^3*A3 + m^3*A2 + m^4*A3 + m^4*A2 + m^4*A2*A3 + 2*m^5*A2*A3 + m^6*A2*A3^2 + m^6*A2^2*A3 + m^6*A1*A2*A3 + m^7*A2^2*A3^2 + m^7*A1*A2*A3^2 + m^7*A1*A2^2*A3 + m^8*A1*A2^2*A3^2
VertexMaslovRank
(-1, -2, -2)-21
(-1, -2, -1)-11
(-1, -1, -2)-11
(-1, -1, -1)01
(0, -2, -2)-11
(0, -2, -1)01
(0, -1, -2)01
(0, 1, 2)61
(0, 2, 1)61
(0, 2, 2)71
(1, 1, 1)61
(1, 1, 2)71
(1, 2, 1)71
(1, 2, 2)81
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Record

FL/HFL Links

orderOption(int) 2213
namestring L10n77{0;0}
statusstring success
slugstring L10n77_0_0_4fab5bbe
result_filestring details/L10n77_0_0_4fab5bbe.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 32
wall_secondsOption(float) 0.001704
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 21
vertex_countOption(int) 14
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 2
alexander_vertex_countOption(int) 2
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10n77_0_0_4fab5bbe"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n77_0_0_4fab5bbe