details/L9n18_1_47a0259a.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-3/2, 3/2) (1, 1/3) x1^(3/2)x2^(-3/2) q^(1/2) 
{"0": [-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^(3/2)*x2^(-3/2) + (q^(-3/2))*x1^(5/2)*x2^(-7/2) + (-q^(-9/2))*x1^(7/2)*x2^(-11/2) + (q^(-3/2))*x1^(7/2)*x2^(-5/2) + (q^(-17/2))*x1^(9/2)*x2^(-15/2) + (-q^(-11/2))*x1^(9/2)*x2^(-9/2) + (-q^(-27/2))*x1^(11/2)*x2^(-19/2) + (q^(-21/2))*x1^(11/2)*x2^(-13/2) + (-q^(-9/2))*x1^(11/2)*x2^(-7/2) + (q^(-39/2))*x1^(13/2)*x2^(-23/2) + (-q^(-33/2))*x1^(13/2)*x2^(-17/2) + (q^(-21/2))*x1^(13/2)*x2^(-11/2) + (-q^(-53/2))*x1^(15/2)*x2^(-27/2) + (q^(-47/2))*x1^(15/2)*x2^(-21/2) + (-q^(-35/2))*x1^(15/2)*x2^(-15/2) + (q^(-17/2))*x1^(15/2)*x2^(-9/2) + (q^(-69/2))*x1^(17/2)*x2^(-31/2) + (-q^(-63/2))*x1^(17/2)*x2^(-25/2) + (q^(-51/2))*x1^(17/2)*x2^(-19/2) + (-q^(-33/2))*x1^(17/2)*x2^(-13/2) + (-q^(-87/2))*x1^(19/2)*x2^(-35/2) + (q^(-81/2))*x1^(19/2)*x2^(-29/2) + (-q^(-69/2))*x1^(19/2)*x2^(-23/2) + (q^(-51/2))*x1^(19/2)*x2^(-17/2) + (-q^(-27/2))*x1^(19/2)*x2^(-11/2)
(-1/2, -1/2) (1, 1) x1^(1/2)x2^(1/2) q^(-9/2) 
{"0": [-1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1, 1, -1]}
 
(-q^(-9/2))*x1^(-7/2)*x2^(17/2) + (q^(-3/2))*x1^(-5/2)*x2^(13/2) + (-q^(3/2))*x1^(-5/2)*x2^(19/2) + (-q^(1/2))*x1^(-3/2)*x2^(9/2) + (q^(7/2))*x1^(-3/2)*x2^(15/2) + (q^(3/2))*x1^(-1/2)*x2^(5/2) + (-q^(9/2))*x1^(-1/2)*x2^(11/2) + (q^(21/2))*x1^(-1/2)*x2^(17/2) + (-q^(3/2))*x1^(1/2)*x2^(1/2) + (q^(9/2))*x1^(1/2)*x2^(7/2) + (-q^(21/2))*x1^(1/2)*x2^(13/2) + (q^(39/2))*x1^(1/2)*x2^(19/2) + (-q^(7/2))*x1^(3/2)*x2^(3/2) + (q^(19/2))*x1^(3/2)*x2^(9/2) + (-q^(37/2))*x1^(3/2)*x2^(15/2) + (q^(3/2))*x1^(5/2)*x2^(-1/2) + (-q^(15/2))*x1^(5/2)*x2^(5/2) + (q^(33/2))*x1^(5/2)*x2^(11/2) + (-q^(57/2))*x1^(5/2)*x2^(17/2) + (q^(9/2))*x1^(7/2)*x2^(1/2) + (-q^(27/2))*x1^(7/2)*x2^(7/2) + (q^(51/2))*x1^(7/2)*x2^(13/2) + (-q^(81/2))*x1^(7/2)*x2^(19/2) + (-q^(1/2))*x1^(9/2)*x2^(-3/2) + (q^(19/2))*x1^(9/2)*x2^(3/2) + (-q^(43/2))*x1^(9/2)*x2^(9/2) + (q^(73/2))*x1^(9/2)*x2^(15/2) + (-q^(9/2))*x1^(11/2)*x2^(-1/2) + (q^(33/2))*x1^(11/2)*x2^(5/2) + (-q^(63/2))*x1^(11/2)*x2^(11/2) + (q^(99/2))*x1^(11/2)*x2^(17/2) + (q^(-3/2))*x1^(13/2)*x2^(-5/2) + (-q^(21/2))*x1^(13/2)*x2^(1/2) + (q^(51/2))*x1^(13/2)*x2^(7/2) + (-q^(87/2))*x1^(13/2)*x2^(13/2) + (q^(129/2))*x1^(13/2)*x2^(19/2) + (q^(7/2))*x1^(15/2)*x2^(-3/2) + (-q^(37/2))*x1^(15/2)*x2^(3/2) + (q^(73/2))*x1^(15/2)*x2^(9/2) + (-q^(115/2))*x1^(15/2)*x2^(15/2) + (-q^(-9/2))*x1^(17/2)*x2^(-7/2) + (q^(21/2))*x1^(17/2)*x2^(-1/2) + (-q^(57/2))*x1^(17/2)*x2^(5/2) + (q^(99/2))*x1^(17/2)*x2^(11/2) + (-q^(147/2))*x1^(17/2)*x2^(17/2) + (-q^(3/2))*x1^(19/2)*x2^(-5/2) + (q^(39/2))*x1^(19/2)*x2^(1/2) + (-q^(81/2))*x1^(19/2)*x2^(7/2) + (q^(129/2))*x1^(19/2)*x2^(13/2) + (-q^(183/2))*x1^(19/2)*x2^(19/2)
(-3/2, 3/2) (1, 1/3) x1^(3/2)x2^(-3/2) q^(1/2) 
{"0": [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^(3/2)*x2^(-3/2) + (q^(-3/2))*x1^(5/2)*x2^(-7/2) + (-q^(-9/2))*x1^(7/2)*x2^(-11/2) + (q^(-3/2))*x1^(7/2)*x2^(-5/2) + (q^(-17/2))*x1^(9/2)*x2^(-15/2) + (-q^(-11/2))*x1^(9/2)*x2^(-9/2) + (-q^(-27/2))*x1^(11/2)*x2^(-19/2) + (q^(-21/2))*x1^(11/2)*x2^(-13/2) + (-q^(-9/2))*x1^(11/2)*x2^(-7/2) + (q^(-39/2))*x1^(13/2)*x2^(-23/2) + (-q^(-33/2))*x1^(13/2)*x2^(-17/2) + (q^(-21/2))*x1^(13/2)*x2^(-11/2) + (-q^(-53/2))*x1^(15/2)*x2^(-27/2) + (q^(-47/2))*x1^(15/2)*x2^(-21/2) + (-q^(-35/2))*x1^(15/2)*x2^(-15/2) + (q^(-17/2))*x1^(15/2)*x2^(-9/2) + (q^(-69/2))*x1^(17/2)*x2^(-31/2) + (-q^(-63/2))*x1^(17/2)*x2^(-25/2) + (q^(-51/2))*x1^(17/2)*x2^(-19/2) + (-q^(-33/2))*x1^(17/2)*x2^(-13/2) + (-q^(-87/2))*x1^(19/2)*x2^(-35/2) + (q^(-81/2))*x1^(19/2)*x2^(-29/2) + (-q^(-69/2))*x1^(19/2)*x2^(-23/2) + (q^(-51/2))*x1^(19/2)*x2^(-17/2) + (-q^(-27/2))*x1^(19/2)*x2^(-11/2)
(-1/2, -1/2) (1, 1) x1^(1/2)x2^(1/2) q^(-9/2) 
{"0": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
 
(-q^(-9/2))*x1^(-7/2)*x2^(17/2) + (q^(-3/2))*x1^(-5/2)*x2^(13/2) + (-q^(3/2))*x1^(-5/2)*x2^(19/2) + (-q^(1/2))*x1^(-3/2)*x2^(9/2) + (q^(7/2))*x1^(-3/2)*x2^(15/2) + (q^(3/2))*x1^(-1/2)*x2^(5/2) + (-q^(9/2))*x1^(-1/2)*x2^(11/2) + (q^(21/2))*x1^(-1/2)*x2^(17/2) + (-q^(3/2))*x1^(1/2)*x2^(1/2) + (q^(9/2))*x1^(1/2)*x2^(7/2) + (-q^(21/2))*x1^(1/2)*x2^(13/2) + (q^(39/2))*x1^(1/2)*x2^(19/2) + (-q^(7/2))*x1^(3/2)*x2^(3/2) + (q^(19/2))*x1^(3/2)*x2^(9/2) + (-q^(37/2))*x1^(3/2)*x2^(15/2) + (q^(3/2))*x1^(5/2)*x2^(-1/2) + (-q^(15/2))*x1^(5/2)*x2^(5/2) + (q^(33/2))*x1^(5/2)*x2^(11/2) + (-q^(57/2))*x1^(5/2)*x2^(17/2) + (q^(9/2))*x1^(7/2)*x2^(1/2) + (-q^(27/2))*x1^(7/2)*x2^(7/2) + (q^(51/2))*x1^(7/2)*x2^(13/2) + (-q^(81/2))*x1^(7/2)*x2^(19/2) + (-q^(1/2))*x1^(9/2)*x2^(-3/2) + (q^(19/2))*x1^(9/2)*x2^(3/2) + (-q^(43/2))*x1^(9/2)*x2^(9/2) + (q^(73/2))*x1^(9/2)*x2^(15/2) + (-q^(9/2))*x1^(11/2)*x2^(-1/2) + (q^(33/2))*x1^(11/2)*x2^(5/2) + (-q^(63/2))*x1^(11/2)*x2^(11/2) + (q^(99/2))*x1^(11/2)*x2^(17/2) + (q^(-3/2))*x1^(13/2)*x2^(-5/2) + (-q^(21/2))*x1^(13/2)*x2^(1/2) + (q^(51/2))*x1^(13/2)*x2^(7/2) + (-q^(87/2))*x1^(13/2)*x2^(13/2) + (q^(129/2))*x1^(13/2)*x2^(19/2) + (q^(7/2))*x1^(15/2)*x2^(-3/2) + (-q^(37/2))*x1^(15/2)*x2^(3/2) + (q^(73/2))*x1^(15/2)*x2^(9/2) + (-q^(115/2))*x1^(15/2)*x2^(15/2) + (-q^(-9/2))*x1^(17/2)*x2^(-7/2) + (q^(21/2))*x1^(17/2)*x2^(-1/2) + (-q^(57/2))*x1^(17/2)*x2^(5/2) + (q^(99/2))*x1^(17/2)*x2^(11/2) + (-q^(147/2))*x1^(17/2)*x2^(17/2) + (-q^(3/2))*x1^(19/2)*x2^(-5/2) + (q^(39/2))*x1^(19/2)*x2^(1/2) + (-q^(81/2))*x1^(19/2)*x2^(7/2) + (q^(129/2))*x1^(19/2)*x2^(13/2) + (-q^(183/2))*x1^(19/2)*x2^(19/2)
(-1/2, -1/2) (1, 1) x1^(1/2)x2^(1/2) q^(-9/2) 
{"0": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "1": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
 
(-q^(-9/2))*x1^(-7/2)*x2^(17/2) + (q^(-3/2))*x1^(-5/2)*x2^(13/2) + (-q^(3/2))*x1^(-5/2)*x2^(19/2) + (-q^(1/2))*x1^(-3/2)*x2^(9/2) + (q^(7/2))*x1^(-3/2)*x2^(15/2) + (q^(3/2))*x1^(-1/2)*x2^(5/2) + (-q^(9/2))*x1^(-1/2)*x2^(11/2) + (q^(21/2))*x1^(-1/2)*x2^(17/2) + (-q^(3/2))*x1^(1/2)*x2^(1/2) + (q^(9/2))*x1^(1/2)*x2^(7/2) + (-q^(21/2))*x1^(1/2)*x2^(13/2) + (q^(39/2))*x1^(1/2)*x2^(19/2) + (-q^(7/2))*x1^(3/2)*x2^(3/2) + (q^(19/2))*x1^(3/2)*x2^(9/2) + (-q^(37/2))*x1^(3/2)*x2^(15/2) + (q^(3/2))*x1^(5/2)*x2^(-1/2) + (-q^(15/2))*x1^(5/2)*x2^(5/2) + (q^(33/2))*x1^(5/2)*x2^(11/2) + (-q^(57/2))*x1^(5/2)*x2^(17/2) + (q^(9/2))*x1^(7/2)*x2^(1/2) + (-q^(27/2))*x1^(7/2)*x2^(7/2) + (q^(51/2))*x1^(7/2)*x2^(13/2) + (-q^(81/2))*x1^(7/2)*x2^(19/2) + (-q^(1/2))*x1^(9/2)*x2^(-3/2) + (q^(19/2))*x1^(9/2)*x2^(3/2) + (-q^(43/2))*x1^(9/2)*x2^(9/2) + (q^(73/2))*x1^(9/2)*x2^(15/2) + (-q^(9/2))*x1^(11/2)*x2^(-1/2) + (q^(33/2))*x1^(11/2)*x2^(5/2) + (-q^(63/2))*x1^(11/2)*x2^(11/2) + (q^(99/2))*x1^(11/2)*x2^(17/2) + (q^(-3/2))*x1^(13/2)*x2^(-5/2) + (-q^(21/2))*x1^(13/2)*x2^(1/2) + (q^(51/2))*x1^(13/2)*x2^(7/2) + (-q^(87/2))*x1^(13/2)*x2^(13/2) + (q^(129/2))*x1^(13/2)*x2^(19/2) + (q^(7/2))*x1^(15/2)*x2^(-3/2) + (-q^(37/2))*x1^(15/2)*x2^(3/2) + (q^(73/2))*x1^(15/2)*x2^(9/2) + (-q^(115/2))*x1^(15/2)*x2^(15/2) + (-q^(-9/2))*x1^(17/2)*x2^(-7/2) + (q^(21/2))*x1^(17/2)*x2^(-1/2) + (-q^(57/2))*x1^(17/2)*x2^(5/2) + (q^(99/2))*x1^(17/2)*x2^(11/2) + (-q^(147/2))*x1^(17/2)*x2^(17/2) + (-q^(3/2))*x1^(19/2)*x2^(-5/2) + (q^(39/2))*x1^(19/2)*x2^(1/2) + (-q^(81/2))*x1^(19/2)*x2^(7/2) + (q^(129/2))*x1^(19/2)*x2^(13/2) + (-q^(183/2))*x1^(19/2)*x2^(19/2)
(3/2, -3/2) x1^(-3/2)x2^(3/2) q^(1/2) 
(-q^(1/2))*x1^(-3/2)*x2^(3/2) + (q^(-3/2))*x1^(-5/2)*x2^(7/2) + (-q^(-9/2))*x1^(-7/2)*x2^(11/2) + (q^(-3/2))*x1^(-7/2)*x2^(5/2) + (q^(-17/2))*x1^(-9/2)*x2^(15/2) + (-q^(-11/2))*x1^(-9/2)*x2^(9/2) + (-q^(-27/2))*x1^(-11/2)*x2^(19/2) + (q^(-21/2))*x1^(-11/2)*x2^(13/2) + (-q^(-9/2))*x1^(-11/2)*x2^(7/2) + (q^(-39/2))*x1^(-13/2)*x2^(23/2) + (-q^(-33/2))*x1^(-13/2)*x2^(17/2) + (q^(-21/2))*x1^(-13/2)*x2^(11/2) + (-q^(-53/2))*x1^(-15/2)*x2^(27/2) + (q^(-47/2))*x1^(-15/2)*x2^(21/2) + (-q^(-35/2))*x1^(-15/2)*x2^(15/2) + (q^(-17/2))*x1^(-15/2)*x2^(9/2) + (q^(-69/2))*x1^(-17/2)*x2^(31/2) + (-q^(-63/2))*x1^(-17/2)*x2^(25/2) + (q^(-51/2))*x1^(-17/2)*x2^(19/2) + (-q^(-33/2))*x1^(-17/2)*x2^(13/2) + (-q^(-87/2))*x1^(-19/2)*x2^(35/2) + (q^(-81/2))*x1^(-19/2)*x2^(29/2) + (-q^(-69/2))*x1^(-19/2)*x2^(23/2) + (q^(-51/2))*x1^(-19/2)*x2^(17/2) + (-q^(-27/2))*x1^(-19/2)*x2^(11/2)
(1/2, 1/2) x1^(-1/2)x2^(-1/2) q^(-9/2) 
(-q^(-9/2))*x1^(7/2)*x2^(-17/2) + (q^(-3/2))*x1^(5/2)*x2^(-13/2) + (-q^(3/2))*x1^(5/2)*x2^(-19/2) + (-q^(1/2))*x1^(3/2)*x2^(-9/2) + (q^(7/2))*x1^(3/2)*x2^(-15/2) + (q^(3/2))*x1^(1/2)*x2^(-5/2) + (-q^(9/2))*x1^(1/2)*x2^(-11/2) + (q^(21/2))*x1^(1/2)*x2^(-17/2) + (-q^(3/2))*x1^(-1/2)*x2^(-1/2) + (q^(9/2))*x1^(-1/2)*x2^(-7/2) + (-q^(21/2))*x1^(-1/2)*x2^(-13/2) + (q^(39/2))*x1^(-1/2)*x2^(-19/2) + (-q^(7/2))*x1^(-3/2)*x2^(-3/2) + (q^(19/2))*x1^(-3/2)*x2^(-9/2) + (-q^(37/2))*x1^(-3/2)*x2^(-15/2) + (q^(3/2))*x1^(-5/2)*x2^(1/2) + (-q^(15/2))*x1^(-5/2)*x2^(-5/2) + (q^(33/2))*x1^(-5/2)*x2^(-11/2) + (-q^(57/2))*x1^(-5/2)*x2^(-17/2) + (q^(9/2))*x1^(-7/2)*x2^(-1/2) + (-q^(27/2))*x1^(-7/2)*x2^(-7/2) + (q^(51/2))*x1^(-7/2)*x2^(-13/2) + (-q^(81/2))*x1^(-7/2)*x2^(-19/2) + (-q^(1/2))*x1^(-9/2)*x2^(3/2) + (q^(19/2))*x1^(-9/2)*x2^(-3/2) + (-q^(43/2))*x1^(-9/2)*x2^(-9/2) + (q^(73/2))*x1^(-9/2)*x2^(-15/2) + (-q^(9/2))*x1^(-11/2)*x2^(1/2) + (q^(33/2))*x1^(-11/2)*x2^(-5/2) + (-q^(63/2))*x1^(-11/2)*x2^(-11/2) + (q^(99/2))*x1^(-11/2)*x2^(-17/2) + (q^(-3/2))*x1^(-13/2)*x2^(5/2) + (-q^(21/2))*x1^(-13/2)*x2^(-1/2) + (q^(51/2))*x1^(-13/2)*x2^(-7/2) + (-q^(87/2))*x1^(-13/2)*x2^(-13/2) + (q^(129/2))*x1^(-13/2)*x2^(-19/2) + (q^(7/2))*x1^(-15/2)*x2^(3/2) + (-q^(37/2))*x1^(-15/2)*x2^(-3/2) + (q^(73/2))*x1^(-15/2)*x2^(-9/2) + (-q^(115/2))*x1^(-15/2)*x2^(-15/2) + (-q^(-9/2))*x1^(-17/2)*x2^(7/2) + (q^(21/2))*x1^(-17/2)*x2^(1/2) + (-q^(57/2))*x1^(-17/2)*x2^(-5/2) + (q^(99/2))*x1^(-17/2)*x2^(-11/2) + (-q^(147/2))*x1^(-17/2)*x2^(-17/2) + (-q^(3/2))*x1^(-19/2)*x2^(5/2) + (q^(39/2))*x1^(-19/2)*x2^(-1/2) + (-q^(81/2))*x1^(-19/2)*x2^(-7/2) + (q^(129/2))*x1^(-19/2)*x2^(-13/2) + (-q^(183/2))*x1^(-19/2)*x2^(-19/2)

Braid

Braid word Components Crossings Strands
[2, -3, 2, 3, 1, 2, -3, 2, 3, 1] 2 10 4

Multivariable Alexander polynomial

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

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-202-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, -1) yes
(3, -3) yes
(1, 1) yes
(-3, 3) yes
Dual Thurston polygon0505h1h2

HFL polytope

Poincaré polynomial
m^(-4)*A1^(-1)*A2^(-1) + m^(-3)*A1^(-1) + m^(-3)*A2^(-1) + m^(-2)*A1^(-2)*A2 + 2*m^(-2) + m^(-2)*A1*A2^(-2) + m^(-1)*A1^(-2)*A2^2 + m^(-1)*A1^(-1)*A2 + m^(-1)*A2 + m^(-1)*A1*A2^(-1) + m^(-1)*A1 + m^(-1)*A1^2*A2^(-2) + A1^(-1)*A2^2 + A1*A2 + A1^2*A2^(-1)
VertexMaslovRank
(-2, 1)-21
(-1, -1)-41
(1, -2)-21
(2, -2)-11
(2, -1)01
(1, 1)01
(-1, 2)01
(-2, 2)-11
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 178
namestring L9n18{1}
statusstring success
slugstring L9n18_1_47a0259a
result_filestring details/L9n18_1_47a0259a.json
complexity_scoreOption(int) 162
strandsOption(int) null
crossingsOption(int) 9
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 16
wall_secondsOption(float) 0.001608
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 15
vertex_countOption(int) 8
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 4
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 7
detailsRowRef(FLHFLLinks) 
{
  "dataset": "FLHFLLinks",
  "key": "L9n18_1_47a0259a"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L9n18_1_47a0259a