L11n133{0} - HFL and FL

details/L11n133_0_0249c8cf.json

F_L expansions

Newt(Δ_L) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle F_L

Newt(Δ_L) vertex	Exposing functional	Leading x-power	Leading q-power	Inversion datum	Inversion cycle	F_L
`(-1, -3)`	`(1, 1)`	`x1^(1)x2^(3)`	`q^(-27/2)`	`{"0": [1, -1, 1, -1, -1, -1], "1": [-1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1]}`		`(-q^(-9/2))x1x2^(3) + (q^(-13/2))x1^(2)x2^(5) + (-q^(-15/2))x1^(2)x2^(6) + (q^(-17/2))x1^(2)x2^(7) + (-q^(-19/2))x1^(3)x2^(7) + (q^(-21/2) + q^(-23/2))x1^(3)x2^(8) + (-2q^(-25/2))x1^(3)x2^(9) + (q^(-27/2))x1^(4)*x2^(9)`
`(1, 3)`		`x1^(-1)x2^(-3)`	`q^(-27/2)`			`(-q^(-9/2))x1^(-1)x2^(-3) + (q^(-13/2))x1^(-2)x2^(-5) + (-q^(-15/2))x1^(-2)x2^(-6) + (q^(-17/2))x1^(-2)x2^(-7) + (-q^(-19/2))x1^(-3)x2^(-7) + (q^(-21/2) + q^(-23/2))x1^(-3)x2^(-8) + (-2q^(-25/2))x1^(-3)x2^(-9) + (q^(-27/2))x1^(-4)*x2^(-9)`

(-1, -3)

(1, 1)

x1^(1)x2^(3)

q^(-27/2)

{"0": [1, -1, 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*x2^(3) + (q^(-13/2))*x1^(2)*x2^(5) + (-q^(-15/2))*x1^(2)*x2^(6) + (q^(-17/2))*x1^(2)*x2^(7) + (-q^(-19/2))*x1^(3)*x2^(7) + (q^(-21/2) + q^(-23/2))*x1^(3)*x2^(8) + (-2*q^(-25/2))*x1^(3)*x2^(9) + (q^(-27/2))*x1^(4)*x2^(9)

(1, 3)

x1^(-1)x2^(-3)

q^(-27/2)

(-q^(-9/2))*x1^(-1)*x2^(-3) + (q^(-13/2))*x1^(-2)*x2^(-5) + (-q^(-15/2))*x1^(-2)*x2^(-6) + (q^(-17/2))*x1^(-2)*x2^(-7) + (-q^(-19/2))*x1^(-3)*x2^(-7) + (q^(-21/2) + q^(-23/2))*x1^(-3)*x2^(-8) + (-2*q^(-25/2))*x1^(-3)*x2^(-9) + (q^(-27/2))*x1^(-4)*x2^(-9)

Braid

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

Multivariable Alexander polynomial

Δ_L
`-A1A2^(3) - A2 + 1 - A2^(-1) - A1^(-1)A2^(-3)`

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

Dual Thurston polytope

Vertex	Dual to fibered face
`(-2, -6)`	yes
`(0, -2)`	yes
`(2, 6)`	yes
`(0, 2)`	yes

HFL polytope

Poincaré polynomial
`m^(-1)A1^(-3/2)A2^(-7/2) + A1^(-3/2)A2^(-5/2) + A1^(-1/2)A2^(-7/2) + mA1^(-1/2)A2^(-5/2) + mA1^(-1/2)A2^(-3/2) + 2m^2A1^(-1/2)A2^(-1/2) + m^2A1^(1/2)A2^(-3/2) + 2m^3A1^(-1/2)A2^(1/2) + 2m^3A1^(1/2)A2^(-1/2) + m^4A1^(-1/2)A2^(3/2) + 2m^4A1^(1/2)A2^(1/2) + m^5A1^(1/2)A2^(3/2) + m^7A1^(1/2)A2^(5/2) + m^8A1^(1/2)A2^(7/2) + m^8A1^(3/2)A2^(5/2) + m^9A1^(3/2)A2^(7/2)`

Vertex	Maslov	Rank
`(-3/2, -7/2)`	-1	1
`(-1/2, -7/2)`	0	1
`(1/2, -3/2)`	2	1
`(3/2, 5/2)`	8	1
`(3/2, 7/2)`	9	1
`(1/2, 7/2)`	8	1
`(-1/2, 3/2)`	4	1
`(-3/2, -5/2)`	0	1

Record

FL/HFL Links

`orderOption(int)`	`1449`
`namestring`	`L11n133{0}`
`statusstring`	`success`
`slugstring`	`L11n133_0_0249c8cf`
`result_filestring`	`details/L11n133_0_0249c8cf.json`
`complexity_scoreOption(int)`	`242`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`11`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`20`
`wall_secondsOption(float)`	`0.002056`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`16`
`vertex_countOption(int)`	`8`
`fibered_vertex_countOption(int)`	`4`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`5`
`alexander_vertex_countOption(int)`	`4`
`alexander_relationstring`	`not_computed`
`fk_countint`	`1`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L11n133_0_0249c8cf" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L11n133_0_0249c8cf`