details/L10n74_1_0_a6318207.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, 1) x1^(1/2)x2^(-1/2)x3^(3/2) q^(1) 
{"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)*x1^(1/2)*x2^(-1/2)*x3^(3/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(5/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(7/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(9/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(11/2) + (q^(2))*x1^(1/2)*x2^(1/2)*x3^(5/2) + (q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(7/2) + (q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(9/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(11/2) + (-q^(4))*x1^(1/2)*x2^(3/2)*x3^(7/2) + (-q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(3/2)*x3^(9/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(3/2)*x3^(11/2) + (q^(7))*x1^(1/2)*x2^(5/2)*x3^(9/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(1/2)*x2^(5/2)*x3^(11/2) + (-q^(11))*x1^(1/2)*x2^(7/2)*x3^(11/2) + (-q^(-3))*x1^(3/2)*x2^(-5/2)*x3^(7/2) + (-q^(-3) - q^(-4))*x1^(3/2)*x2^(-5/2)*x3^(9/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(3/2)*x2^(-5/2)*x3^(11/2) + (q^(-2))*x1^(3/2)*x2^(-3/2)*x3^(7/2) + (2*q^(-2) + q^(-3))*x1^(3/2)*x2^(-3/2)*x3^(9/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(3/2)*x2^(-3/2)*x3^(11/2) + (-1 - q^(-1))*x1^(3/2)*x2^(-1/2)*x3^(9/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(3/2)*x2^(-1/2)*x3^(11/2) + (q^(3) + q^(2) + q)*x1^(3/2)*x2^(1/2)*x3^(11/2) + (-q^(-11))*x1^(5/2)*x2^(-9/2)*x3^(11/2) + (q^(-9) + q^(-10))*x1^(5/2)*x2^(-7/2)*x3^(11/2) + (-q^(-8))*x1^(5/2)*x2^(-5/2)*x3^(11/2)
(1/2, -3/2, 1/2) (1/2, 1, 1/2) x1^(-1/2)x2^(3/2)x3^(-1/2) q^(1) 
{"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^(-11))*x1^(-5/2)*x2^(11/2)*x3^(-9/2) + (q^(-9) + q^(-10))*x1^(-5/2)*x2^(11/2)*x3^(-7/2) + (-q^(-8))*x1^(-5/2)*x2^(11/2)*x3^(-5/2) + (-q^(-3))*x1^(-3/2)*x2^(7/2)*x3^(-5/2) + (q^(-2))*x1^(-3/2)*x2^(7/2)*x3^(-3/2) + (-q^(-3) - q^(-4))*x1^(-3/2)*x2^(9/2)*x3^(-5/2) + (2*q^(-2) + q^(-3))*x1^(-3/2)*x2^(9/2)*x3^(-3/2) + (-1 - q^(-1))*x1^(-3/2)*x2^(9/2)*x3^(-1/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(-3/2)*x2^(11/2)*x3^(-5/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(-3/2)*x2^(11/2)*x3^(-3/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(-3/2)*x2^(11/2)*x3^(-1/2) + (q^(3) + q^(2) + q)*x1^(-3/2)*x2^(11/2)*x3^(1/2) + (-q)*x1^(-1/2)*x2^(3/2)*x3^(-1/2) + (-q)*x1^(-1/2)*x2^(5/2)*x3^(-1/2) + (q^(2))*x1^(-1/2)*x2^(5/2)*x3^(1/2) + (-q)*x1^(-1/2)*x2^(7/2)*x3^(-1/2) + (q^(3) + q^(2))*x1^(-1/2)*x2^(7/2)*x3^(1/2) + (-q^(4))*x1^(-1/2)*x2^(7/2)*x3^(3/2) + (-q)*x1^(-1/2)*x2^(9/2)*x3^(-1/2) + (q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(9/2)*x3^(1/2) + (-q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(9/2)*x3^(3/2) + (q^(7))*x1^(-1/2)*x2^(9/2)*x3^(5/2) + (-q)*x1^(-1/2)*x2^(11/2)*x3^(-1/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(11/2)*x3^(1/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(11/2)*x3^(3/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(-1/2)*x2^(11/2)*x3^(5/2) + (-q^(11))*x1^(-1/2)*x2^(11/2)*x3^(7/2)
(-1/2, 1/2, -3/2) (1, 1, 1) x1^(1/2)x2^(-1/2)x3^(3/2) q^(1) 
{"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)*x1^(1/2)*x2^(-1/2)*x3^(3/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(5/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(7/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(9/2) + (-q)*x1^(1/2)*x2^(-1/2)*x3^(11/2) + (q^(2))*x1^(1/2)*x2^(1/2)*x3^(5/2) + (q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(7/2) + (q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(9/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(1/2)*x3^(11/2) + (-q^(4))*x1^(1/2)*x2^(3/2)*x3^(7/2) + (-q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(3/2)*x3^(9/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(3/2)*x3^(11/2) + (q^(7))*x1^(1/2)*x2^(5/2)*x3^(9/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(1/2)*x2^(5/2)*x3^(11/2) + (-q^(11))*x1^(1/2)*x2^(7/2)*x3^(11/2) + (-q^(-3))*x1^(3/2)*x2^(-5/2)*x3^(7/2) + (-q^(-3) - q^(-4))*x1^(3/2)*x2^(-5/2)*x3^(9/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(3/2)*x2^(-5/2)*x3^(11/2) + (q^(-2))*x1^(3/2)*x2^(-3/2)*x3^(7/2) + (2*q^(-2) + q^(-3))*x1^(3/2)*x2^(-3/2)*x3^(9/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(3/2)*x2^(-3/2)*x3^(11/2) + (-1 - q^(-1))*x1^(3/2)*x2^(-1/2)*x3^(9/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(3/2)*x2^(-1/2)*x3^(11/2) + (q^(3) + q^(2) + q)*x1^(3/2)*x2^(1/2)*x3^(11/2) + (-q^(-11))*x1^(5/2)*x2^(-9/2)*x3^(11/2) + (q^(-9) + q^(-10))*x1^(5/2)*x2^(-7/2)*x3^(11/2) + (-q^(-8))*x1^(5/2)*x2^(-5/2)*x3^(11/2)
(1/2, -3/2, 1/2) (1/2, 1, 1/2) x1^(-1/2)x2^(3/2)x3^(-1/2) q^(1) 
{"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^(-11))*x1^(-5/2)*x2^(11/2)*x3^(-9/2) + (q^(-9) + q^(-10))*x1^(-5/2)*x2^(11/2)*x3^(-7/2) + (-q^(-8))*x1^(-5/2)*x2^(11/2)*x3^(-5/2) + (-q^(-3))*x1^(-3/2)*x2^(7/2)*x3^(-5/2) + (q^(-2))*x1^(-3/2)*x2^(7/2)*x3^(-3/2) + (-q^(-3) - q^(-4))*x1^(-3/2)*x2^(9/2)*x3^(-5/2) + (2*q^(-2) + q^(-3))*x1^(-3/2)*x2^(9/2)*x3^(-3/2) + (-1 - q^(-1))*x1^(-3/2)*x2^(9/2)*x3^(-1/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(-3/2)*x2^(11/2)*x3^(-5/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(-3/2)*x2^(11/2)*x3^(-3/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(-3/2)*x2^(11/2)*x3^(-1/2) + (q^(3) + q^(2) + q)*x1^(-3/2)*x2^(11/2)*x3^(1/2) + (-q)*x1^(-1/2)*x2^(3/2)*x3^(-1/2) + (-q)*x1^(-1/2)*x2^(5/2)*x3^(-1/2) + (q^(2))*x1^(-1/2)*x2^(5/2)*x3^(1/2) + (-q)*x1^(-1/2)*x2^(7/2)*x3^(-1/2) + (q^(3) + q^(2))*x1^(-1/2)*x2^(7/2)*x3^(1/2) + (-q^(4))*x1^(-1/2)*x2^(7/2)*x3^(3/2) + (-q)*x1^(-1/2)*x2^(9/2)*x3^(-1/2) + (q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(9/2)*x3^(1/2) + (-q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(9/2)*x3^(3/2) + (q^(7))*x1^(-1/2)*x2^(9/2)*x3^(5/2) + (-q)*x1^(-1/2)*x2^(11/2)*x3^(-1/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(11/2)*x3^(1/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(11/2)*x3^(3/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(-1/2)*x2^(11/2)*x3^(5/2) + (-q^(11))*x1^(-1/2)*x2^(11/2)*x3^(7/2)
(1/2, -1/2, 3/2) x1^(-1/2)x2^(1/2)x3^(-3/2) q^(1) 
(-q)*x1^(-1/2)*x2^(1/2)*x3^(-3/2) + (-q)*x1^(-1/2)*x2^(1/2)*x3^(-5/2) + (-q)*x1^(-1/2)*x2^(1/2)*x3^(-7/2) + (-q)*x1^(-1/2)*x2^(1/2)*x3^(-9/2) + (-q)*x1^(-1/2)*x2^(1/2)*x3^(-11/2) + (q^(2))*x1^(-1/2)*x2^(-1/2)*x3^(-5/2) + (q^(3) + q^(2))*x1^(-1/2)*x2^(-1/2)*x3^(-7/2) + (q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(-1/2)*x3^(-9/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(-1/2)*x2^(-1/2)*x3^(-11/2) + (-q^(4))*x1^(-1/2)*x2^(-3/2)*x3^(-7/2) + (-q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(-3/2)*x3^(-9/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(-1/2)*x2^(-3/2)*x3^(-11/2) + (q^(7))*x1^(-1/2)*x2^(-5/2)*x3^(-9/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(-1/2)*x2^(-5/2)*x3^(-11/2) + (-q^(11))*x1^(-1/2)*x2^(-7/2)*x3^(-11/2) + (-q^(-3))*x1^(-3/2)*x2^(5/2)*x3^(-7/2) + (-q^(-3) - q^(-4))*x1^(-3/2)*x2^(5/2)*x3^(-9/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(-3/2)*x2^(5/2)*x3^(-11/2) + (q^(-2))*x1^(-3/2)*x2^(3/2)*x3^(-7/2) + (2*q^(-2) + q^(-3))*x1^(-3/2)*x2^(3/2)*x3^(-9/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(-3/2)*x2^(3/2)*x3^(-11/2) + (-1 - q^(-1))*x1^(-3/2)*x2^(1/2)*x3^(-9/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(-3/2)*x2^(1/2)*x3^(-11/2) + (q^(3) + q^(2) + q)*x1^(-3/2)*x2^(-1/2)*x3^(-11/2) + (-q^(-11))*x1^(-5/2)*x2^(9/2)*x3^(-11/2) + (q^(-9) + q^(-10))*x1^(-5/2)*x2^(7/2)*x3^(-11/2) + (-q^(-8))*x1^(-5/2)*x2^(5/2)*x3^(-11/2)
(-1/2, 3/2, -1/2) x1^(1/2)x2^(-3/2)x3^(1/2) q^(1) 
(-q^(-11))*x1^(5/2)*x2^(-11/2)*x3^(9/2) + (q^(-9) + q^(-10))*x1^(5/2)*x2^(-11/2)*x3^(7/2) + (-q^(-8))*x1^(5/2)*x2^(-11/2)*x3^(5/2) + (-q^(-3))*x1^(3/2)*x2^(-7/2)*x3^(5/2) + (q^(-2))*x1^(3/2)*x2^(-7/2)*x3^(3/2) + (-q^(-3) - q^(-4))*x1^(3/2)*x2^(-9/2)*x3^(5/2) + (2*q^(-2) + q^(-3))*x1^(3/2)*x2^(-9/2)*x3^(3/2) + (-1 - q^(-1))*x1^(3/2)*x2^(-9/2)*x3^(1/2) + (-q^(-3) - q^(-4) - q^(-5))*x1^(3/2)*x2^(-11/2)*x3^(5/2) + (q^(-1) + 3*q^(-2) + 2*q^(-3) + q^(-4))*x1^(3/2)*x2^(-11/2)*x3^(3/2) + (-q - 3*1 - 2*q^(-1) - q^(-2))*x1^(3/2)*x2^(-11/2)*x3^(1/2) + (q^(3) + q^(2) + q)*x1^(3/2)*x2^(-11/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(-3/2)*x3^(1/2) + (-q)*x1^(1/2)*x2^(-5/2)*x3^(1/2) + (q^(2))*x1^(1/2)*x2^(-5/2)*x3^(-1/2) + (-q)*x1^(1/2)*x2^(-7/2)*x3^(1/2) + (q^(3) + q^(2))*x1^(1/2)*x2^(-7/2)*x3^(-1/2) + (-q^(4))*x1^(1/2)*x2^(-7/2)*x3^(-3/2) + (-q)*x1^(1/2)*x2^(-9/2)*x3^(1/2) + (q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(-9/2)*x3^(-1/2) + (-q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(-9/2)*x3^(-3/2) + (q^(7))*x1^(1/2)*x2^(-9/2)*x3^(-5/2) + (-q)*x1^(1/2)*x2^(-11/2)*x3^(1/2) + (q^(5) + q^(4) + q^(3) + q^(2))*x1^(1/2)*x2^(-11/2)*x3^(-1/2) + (-q^(8) - q^(7) - 2*q^(6) - q^(5) - q^(4))*x1^(1/2)*x2^(-11/2)*x3^(-3/2) + (q^(10) + q^(9) + q^(8) + q^(7))*x1^(1/2)*x2^(-11/2)*x3^(-5/2) + (-q^(11))*x1^(1/2)*x2^(-11/2)*x3^(-7/2)

Braid

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

Multivariable Alexander polynomial

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

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

FL/HFL Links

orderOption(int) 2203
namestring L10n74{1;0}
statusstring success
slugstring L10n74_1_0_a6318207
result_filestring details/L10n74_1_0_a6318207.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) 0.001689
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_1_0_a6318207"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n74_1_0_a6318207