details/L10n74_0_0_08b8792f.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, -1/2, -3/2) (1, 1/2, 1) x1^(1/2)x2^(1/2)x3^(3/2) q^(-3) 
{"0": [-1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], "2": [-1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(7))*x1^(1/2)*x2^(-7/2)*x3^(11/2) + (q^(3))*x1^(1/2)*x2^(-5/2)*x3^(9/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(1/2)*x2^(-5/2)*x3^(11/2) + (-1)*x1^(1/2)*x2^(-3/2)*x3^(7/2) + (-q^(2) - q - 1)*x1^(1/2)*x2^(-3/2)*x3^(9/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(1/2)*x2^(-3/2)*x3^(11/2) + (q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(5/2) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(7/2) + (1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(9/2) + (q + 1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(11/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(3/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(5/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(7/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(9/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(11/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(3/2)*x2^(-1/2)*x3^(11/2) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(1/2)*x3^(9/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(3/2)*x2^(1/2)*x3^(11/2) + (q^(-6))*x1^(3/2)*x2^(3/2)*x3^(7/2) + (2*q^(-6) + q^(-7))*x1^(3/2)*x2^(3/2)*x3^(9/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(3/2)*x2^(3/2)*x3^(11/2) + (-q^(-7))*x1^(3/2)*x2^(5/2)*x3^(7/2) + (-q^(-7) - q^(-8))*x1^(3/2)*x2^(5/2)*x3^(9/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(5/2)*x3^(11/2) + (-q^(-12))*x1^(5/2)*x2^(5/2)*x3^(11/2) + (q^(-13) + q^(-14))*x1^(5/2)*x2^(7/2)*x3^(11/2) + (-q^(-15))*x1^(5/2)*x2^(9/2)*x3^(11/2)
(-1/2, -3/2, -1/2) (1, 1, 0) x1^(1/2)x2^(3/2)x3^(1/2) q^(-3) 
{"0": [-1, -1, -1, -1], "1": [-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], "2": [-1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(-3))*x1^(1/2)*x2^(3/2)*x3^(1/2) + (q^(-2))*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (-1)*x1^(1/2)*x2^(7/2)*x3^(-3/2) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (q^(3))*x1^(1/2)*x2^(9/2)*x3^(-5/2) + (-q^(2) - q - 1)*x1^(1/2)*x2^(9/2)*x3^(-3/2) + (1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (-q^(7))*x1^(1/2)*x2^(11/2)*x3^(-7/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(1/2)*x2^(11/2)*x3^(-5/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(1/2)*x2^(11/2)*x3^(-3/2) + (q + 1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (q^(-6))*x1^(3/2)*x2^(7/2)*x3^(3/2) + (-q^(-7))*x1^(3/2)*x2^(7/2)*x3^(5/2) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (2*q^(-6) + q^(-7))*x1^(3/2)*x2^(9/2)*x3^(3/2) + (-q^(-7) - q^(-8))*x1^(3/2)*x2^(9/2)*x3^(5/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(3/2)*x2^(11/2)*x3^(3/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(11/2)*x3^(5/2) + (-q^(-12))*x1^(5/2)*x2^(11/2)*x3^(5/2) + (q^(-13) + q^(-14))*x1^(5/2)*x2^(11/2)*x3^(7/2) + (-q^(-15))*x1^(5/2)*x2^(11/2)*x3^(9/2)
(-1/2, -1/2, -3/2) (1, 1/2, 1) x1^(1/2)x2^(1/2)x3^(3/2) q^(-3) 
{"0": [1, -1, -1, -1], "1": [-1, -1, -1, -1, -1, -1, -1, -1, -1, 1], "2": [-1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(7))*x1^(1/2)*x2^(-7/2)*x3^(11/2) + (q^(3))*x1^(1/2)*x2^(-5/2)*x3^(9/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(1/2)*x2^(-5/2)*x3^(11/2) + (-1)*x1^(1/2)*x2^(-3/2)*x3^(7/2) + (-q^(2) - q - 1)*x1^(1/2)*x2^(-3/2)*x3^(9/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(1/2)*x2^(-3/2)*x3^(11/2) + (q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(5/2) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(7/2) + (1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(9/2) + (q + 1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(-1/2)*x3^(11/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(3/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(5/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(7/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(9/2) + (-q^(-3))*x1^(1/2)*x2^(1/2)*x3^(11/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(3/2)*x2^(-1/2)*x3^(11/2) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(1/2)*x3^(9/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(3/2)*x2^(1/2)*x3^(11/2) + (q^(-6))*x1^(3/2)*x2^(3/2)*x3^(7/2) + (2*q^(-6) + q^(-7))*x1^(3/2)*x2^(3/2)*x3^(9/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(3/2)*x2^(3/2)*x3^(11/2) + (-q^(-7))*x1^(3/2)*x2^(5/2)*x3^(7/2) + (-q^(-7) - q^(-8))*x1^(3/2)*x2^(5/2)*x3^(9/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(5/2)*x3^(11/2) + (-q^(-12))*x1^(5/2)*x2^(5/2)*x3^(11/2) + (q^(-13) + q^(-14))*x1^(5/2)*x2^(7/2)*x3^(11/2) + (-q^(-15))*x1^(5/2)*x2^(9/2)*x3^(11/2)
(-1/2, -3/2, -1/2) (1, 1, 0) x1^(1/2)x2^(3/2)x3^(1/2) q^(-3) 
{"0": [1, -1, -1, -1], "1": [-1, -1, 1, 1, 1, -1, -1, -1, -1, 1], "2": [-1, -1, -1, -1, -1, -1, -1, -1]}
 
(-q^(-3))*x1^(1/2)*x2^(3/2)*x3^(1/2) + (q^(-2))*x1^(1/2)*x2^(5/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(5/2)*x3^(1/2) + (-1)*x1^(1/2)*x2^(7/2)*x3^(-3/2) + (q^(-1) + q^(-2))*x1^(1/2)*x2^(7/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(7/2)*x3^(1/2) + (q^(3))*x1^(1/2)*x2^(9/2)*x3^(-5/2) + (-q^(2) - q - 1)*x1^(1/2)*x2^(9/2)*x3^(-3/2) + (1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(9/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(9/2)*x3^(1/2) + (-q^(7))*x1^(1/2)*x2^(11/2)*x3^(-7/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(1/2)*x2^(11/2)*x3^(-5/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(1/2)*x2^(11/2)*x3^(-3/2) + (q + 1 + q^(-1) + q^(-2))*x1^(1/2)*x2^(11/2)*x3^(-1/2) + (-q^(-3))*x1^(1/2)*x2^(11/2)*x3^(1/2) + (q^(-6))*x1^(3/2)*x2^(7/2)*x3^(3/2) + (-q^(-7))*x1^(3/2)*x2^(7/2)*x3^(5/2) + (-q^(-4) - q^(-5))*x1^(3/2)*x2^(9/2)*x3^(1/2) + (2*q^(-6) + q^(-7))*x1^(3/2)*x2^(9/2)*x3^(3/2) + (-q^(-7) - q^(-8))*x1^(3/2)*x2^(9/2)*x3^(5/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(3/2)*x2^(11/2)*x3^(-1/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(3/2)*x2^(11/2)*x3^(1/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(3/2)*x2^(11/2)*x3^(3/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(3/2)*x2^(11/2)*x3^(5/2) + (-q^(-12))*x1^(5/2)*x2^(11/2)*x3^(5/2) + (q^(-13) + q^(-14))*x1^(5/2)*x2^(11/2)*x3^(7/2) + (-q^(-15))*x1^(5/2)*x2^(11/2)*x3^(9/2)
(1/2, 1/2, 3/2) x1^(-1/2)x2^(-1/2)x3^(-3/2) q^(-3) 
(-q^(7))*x1^(-1/2)*x2^(7/2)*x3^(-11/2) + (q^(3))*x1^(-1/2)*x2^(5/2)*x3^(-9/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(-1/2)*x2^(5/2)*x3^(-11/2) + (-1)*x1^(-1/2)*x2^(3/2)*x3^(-7/2) + (-q^(2) - q - 1)*x1^(-1/2)*x2^(3/2)*x3^(-9/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(-1/2)*x2^(3/2)*x3^(-11/2) + (q^(-2))*x1^(-1/2)*x2^(1/2)*x3^(-5/2) + (q^(-1) + q^(-2))*x1^(-1/2)*x2^(1/2)*x3^(-7/2) + (1 + q^(-1) + q^(-2))*x1^(-1/2)*x2^(1/2)*x3^(-9/2) + (q + 1 + q^(-1) + q^(-2))*x1^(-1/2)*x2^(1/2)*x3^(-11/2) + (-q^(-3))*x1^(-1/2)*x2^(-1/2)*x3^(-3/2) + (-q^(-3))*x1^(-1/2)*x2^(-1/2)*x3^(-5/2) + (-q^(-3))*x1^(-1/2)*x2^(-1/2)*x3^(-7/2) + (-q^(-3))*x1^(-1/2)*x2^(-1/2)*x3^(-9/2) + (-q^(-3))*x1^(-1/2)*x2^(-1/2)*x3^(-11/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(-3/2)*x2^(1/2)*x3^(-11/2) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(-1/2)*x3^(-9/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(-3/2)*x2^(-1/2)*x3^(-11/2) + (q^(-6))*x1^(-3/2)*x2^(-3/2)*x3^(-7/2) + (2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-3/2)*x3^(-9/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(-3/2)*x2^(-3/2)*x3^(-11/2) + (-q^(-7))*x1^(-3/2)*x2^(-5/2)*x3^(-7/2) + (-q^(-7) - q^(-8))*x1^(-3/2)*x2^(-5/2)*x3^(-9/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(-3/2)*x2^(-5/2)*x3^(-11/2) + (-q^(-12))*x1^(-5/2)*x2^(-5/2)*x3^(-11/2) + (q^(-13) + q^(-14))*x1^(-5/2)*x2^(-7/2)*x3^(-11/2) + (-q^(-15))*x1^(-5/2)*x2^(-9/2)*x3^(-11/2)
(1/2, 3/2, 1/2) x1^(-1/2)x2^(-3/2)x3^(-1/2) q^(-3) 
(-q^(-3))*x1^(-1/2)*x2^(-3/2)*x3^(-1/2) + (q^(-2))*x1^(-1/2)*x2^(-5/2)*x3^(1/2) + (-q^(-3))*x1^(-1/2)*x2^(-5/2)*x3^(-1/2) + (-1)*x1^(-1/2)*x2^(-7/2)*x3^(3/2) + (q^(-1) + q^(-2))*x1^(-1/2)*x2^(-7/2)*x3^(1/2) + (-q^(-3))*x1^(-1/2)*x2^(-7/2)*x3^(-1/2) + (q^(3))*x1^(-1/2)*x2^(-9/2)*x3^(5/2) + (-q^(2) - q - 1)*x1^(-1/2)*x2^(-9/2)*x3^(3/2) + (1 + q^(-1) + q^(-2))*x1^(-1/2)*x2^(-9/2)*x3^(1/2) + (-q^(-3))*x1^(-1/2)*x2^(-9/2)*x3^(-1/2) + (-q^(7))*x1^(-1/2)*x2^(-11/2)*x3^(7/2) + (q^(6) + q^(5) + q^(4) + q^(3))*x1^(-1/2)*x2^(-11/2)*x3^(5/2) + (-q^(4) - q^(3) - 2*q^(2) - q - 1)*x1^(-1/2)*x2^(-11/2)*x3^(3/2) + (q + 1 + q^(-1) + q^(-2))*x1^(-1/2)*x2^(-11/2)*x3^(1/2) + (-q^(-3))*x1^(-1/2)*x2^(-11/2)*x3^(-1/2) + (q^(-6))*x1^(-3/2)*x2^(-7/2)*x3^(-3/2) + (-q^(-7))*x1^(-3/2)*x2^(-7/2)*x3^(-5/2) + (-q^(-4) - q^(-5))*x1^(-3/2)*x2^(-9/2)*x3^(-1/2) + (2*q^(-6) + q^(-7))*x1^(-3/2)*x2^(-9/2)*x3^(-3/2) + (-q^(-7) - q^(-8))*x1^(-3/2)*x2^(-9/2)*x3^(-5/2) + (q^(-1) + q^(-2) + q^(-3))*x1^(-3/2)*x2^(-11/2)*x3^(1/2) + (-q^(-3) - 3*q^(-4) - 2*q^(-5) - q^(-6))*x1^(-3/2)*x2^(-11/2)*x3^(-1/2) + (q^(-5) + 3*q^(-6) + 2*q^(-7) + q^(-8))*x1^(-3/2)*x2^(-11/2)*x3^(-3/2) + (-q^(-7) - q^(-8) - q^(-9))*x1^(-3/2)*x2^(-11/2)*x3^(-5/2) + (-q^(-12))*x1^(-5/2)*x2^(-11/2)*x3^(-5/2) + (q^(-13) + q^(-14))*x1^(-5/2)*x2^(-11/2)*x3^(-7/2) + (-q^(-15))*x1^(-5/2)*x2^(-11/2)*x3^(-9/2)

Braid

Braid word Components Crossings Strands
[-2, 3, -2, -2, -2, -1, -2, -2, -3, -3, -1] 3 11 4

Multivariable Alexander polynomial

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

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, -1, -1) yes
(1, 3, 1) yes
(-1, -1, -3) yes
(1, 1, 1) yes
(-1, -3, -1) yes
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HFL polytope

Poincaré polynomial
m^(-2)*A1^(-1)*A2^(-2)*A3^(-1) + m^(-2)*A1^(-1)*A2^(-1)*A3^(-2) + m^(-1)*A1^(-1)*A2^(-2) + 3*m^(-1)*A1^(-1)*A2^(-1)*A3^(-1) + m^(-1)*A1^(-1)*A3^(-2) + m^(-1)*A2^(-2)*A3^(-1) + m^(-1)*A2^(-1)*A3^(-2) + 2*A1^(-1)*A2^(-1) + 2*A1^(-1)*A3^(-1) + A2^(-2) + 3*A2^(-1)*A3^(-1) + A2^(-1) + A3^(-2) + A3^(-1) + m*A1^(-1) + 3*m*A2^(-1) + m*A2^(-1)*A3 + 3*m*A3^(-1) + 2*m + m*A2*A3^(-1) + m^2*A2^(-1)*A3 + 4*m^2 + m^2*A3 + m^2*A2*A3^(-1) + m^2*A2 + 3*m^3*A3 + 3*m^3*A2 + m^3*A1 + m^4*A3^2 + 3*m^4*A2*A3 + m^4*A2^2 + 2*m^4*A1*A3 + 2*m^4*A1*A2 + m^5*A2*A3^2 + m^5*A2^2*A3 + m^5*A1*A3^2 + 3*m^5*A1*A2*A3 + m^5*A1*A2^2 + m^6*A1*A2*A3^2 + m^6*A1*A2^2*A3
VertexMaslovRank
(-1, -2, -1)-21
(-1, -2, 0)-11
(-1, -1, -2)-21
(-1, 0, -2)-11
(-1, 0, 0)11
(0, -2, -1)-11
(0, -2, 0)01
(0, -1, -2)-11
(0, 0, -2)01
(0, 0, 2)41
(0, 1, 2)51
(0, 2, 0)41
(0, 2, 1)51
(1, 0, 0)31
(1, 0, 2)51
(1, 1, 2)61
(1, 2, 0)51
(1, 2, 1)61
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Record

FL/HFL Links

orderOption(int) 2201
namestring L10n74{0;0}
statusstring success
slugstring L10n74_0_0_08b8792f
result_filestring details/L10n74_0_0_08b8792f.json
complexity_scoreOption(int) 300
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 3
girthOption(int) 6
total_rankOption(int) 64
wall_secondsOption(float) 0.001674
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 3
support_sizeOption(int) 33
vertex_countOption(int) 18
fibered_vertex_countOption(int) 6
polytope_statusstring computed
alexander_support_sizeOption(int) 6
alexander_vertex_countOption(int) 6
alexander_relationstring not_computed
fk_countint 4
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L10n74_0_0_08b8792f"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n74_0_0_08b8792f