L10a118{0} - HFL and FL

details/L10a118_0_7ea812e2.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	F_L
`(-2, -2)`	`(1, 1)`	`x1^(2)x2^(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^(2)x2^(2) + (q^(-11/2))x1^(3)x2^(3) + (-q^(-27/2))x1^(7)x2^(7) + (q^(-33/2))x1^(8)x2^(8)`
`(-2, -2)`	`(1, 1)`	`x1^(2)x2^(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^(2)x2^(2) + (q^(-11/2))x1^(3)x2^(3) + (-q^(-27/2))x1^(7)x2^(7) + (q^(-33/2))x1^(8)x2^(8)`
`(2, 2)`		`x1^(-2)x2^(-2)`	`q^(-9/2)`		`(-q^(-9/2))x1^(-2)x2^(-2) + (q^(-11/2))x1^(-3)x2^(-3) + (-q^(-27/2))x1^(-7)x2^(-7) + (q^(-33/2))x1^(-8)x2^(-8)`

(-2, -2)

(1, 1)

x1^(2)x2^(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^(2)*x2^(2) + (q^(-11/2))*x1^(3)*x2^(3) + (-q^(-27/2))*x1^(7)*x2^(7) + (q^(-33/2))*x1^(8)*x2^(8)

(-2, -2)

(1, 1)

x1^(2)x2^(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^(2)*x2^(2) + (q^(-11/2))*x1^(3)*x2^(3) + (-q^(-27/2))*x1^(7)*x2^(7) + (q^(-33/2))*x1^(8)*x2^(8)

(2, 2)

x1^(-2)x2^(-2)

q^(-9/2)

(-q^(-9/2))*x1^(-2)*x2^(-2) + (q^(-11/2))*x1^(-3)*x2^(-3) + (-q^(-27/2))*x1^(-7)*x2^(-7) + (q^(-33/2))*x1^(-8)*x2^(-8)

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

Δ_L
`-A1^(2)A2^(2) - A1A2 - 1 - A1^(-1)A2^(-1) - A1^(-2)A2^(-2)`

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

Vertex	Dual to fibered face
`(-4, -4)`	yes
`(4, 4)`	yes

Poincaré polynomial
`m^(-1)A1^(-5/2)A2^(-5/2) + A1^(-5/2)A2^(-3/2) + A1^(-3/2)A2^(-5/2) + 2mA1^(-3/2)A2^(-3/2) + m^2A1^(-3/2)A2^(-1/2) + m^2A1^(-1/2)A2^(-3/2) + 2m^3A1^(-1/2)A2^(-1/2) + m^4A1^(-1/2)A2^(1/2) + m^4A1^(1/2)A2^(-1/2) + 2m^5A1^(1/2)A2^(1/2) + m^6A1^(1/2)A2^(3/2) + m^6A1^(3/2)A2^(1/2) + 2m^7A1^(3/2)A2^(3/2) + m^8A1^(3/2)A2^(5/2) + m^8A1^(5/2)A2^(3/2) + m^9A1^(5/2)A2^(5/2)`

`orderOption(int)`	`277`
`namestring`	`L10a118{0}`
`statusstring`	`success`
`slugstring`	`L10a118_0_7ea812e2`
`result_filestring`	`details/L10a118_0_7ea812e2.json`
`complexity_scoreOption(int)`	`200`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`2`
`girthOption(int)`	`4`
`total_rankOption(int)`	`20`
`wall_secondsOption(float)`	`0.001516`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`16`
`vertex_countOption(int)`	`6`
`fibered_vertex_countOption(int)`	`2`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`5`
`alexander_vertex_countOption(int)`	`2`
`alexander_relationstring`	`not_computed`
`fk_countint`	`2`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10a118_0_7ea812e2" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10a118_0_7ea812e2`