L11a502{1;1} - HFL and FL

details/L11a502_1_1_b362e881.json

Multivariable Alexander polynomial

Δ_L
A1A2A3^(3/2) - A1A2A3^(1/2) + A1A2A3^(-1/2) - A1A2A3^(-3/2) - A1A3^(3/2) + 2A1A3^(1/2) - 2A1A3^(-1/2) + 2A1A3^(-3/2) - 2A2A3^(3/2) + 2A2A3^(1/2) - 2A2A3^(-1/2) + A2A3^(-3/2) + 3A3^(3/2) - 4A3^(1/2) + 4A3^(-1/2) - 3A3^(-3/2) - A2^(-1)A3^(3/2) + 2A2^(-1)A3^(1/2) - 2A2^(-1)A3^(-1/2) + 2A2^(-1)A3^(-3/2) - 2A1^(-1)A3^(3/2) + 2A1^(-1)A3^(1/2) - 2A1^(-1)A3^(-1/2) + A1^(-1)A3^(-3/2) + A1^(-1)A2^(-1)A3^(3/2) - A1^(-1)A2^(-1)A3^(1/2) + A1^(-1)A2^(-1)A3^(-1/2) - A1^(-1)A2^(-1)A3^(-3/2)

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

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Dual Thurston polytope

Vertex	Dual to fibered face
`(2, 2, 3)`	yes
`(0, 2, -3)`	yes
`(0, 2, 3)`	no
`(-2, 0, -3)`	yes
`(0, -2, -3)`	no
`(-2, 0, 3)`	no
`(0, -2, 3)`	yes
`(2, 2, -3)`	yes
`(2, 0, -3)`	no
`(-2, -2, -3)`	yes
`(-2, -2, 3)`	yes
`(2, 0, 3)`	yes

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HFL polytope

Poincaré polynomial
m^(-6)A1^(-3/2)A2^(-3/2)A3^(-2) + 2m^(-5)A1^(-3/2)A2^(-3/2)A3^(-1) + 2m^(-5)A1^(-3/2)A2^(-1/2)A3^(-2) + 3m^(-5)A1^(-1/2)A2^(-3/2)A3^(-2) + 2m^(-4)A1^(-3/2)A2^(-3/2) + 5m^(-4)A1^(-3/2)A2^(-1/2)A3^(-1) + m^(-4)A1^(-3/2)A2^(1/2)A3^(-2) + 6m^(-4)A1^(-1/2)A2^(-3/2)A3^(-1) + 7m^(-4)A1^(-1/2)A2^(-1/2)A3^(-2) + 2m^(-4)A1^(1/2)A2^(-3/2)A3^(-2) + 2m^(-3)A1^(-3/2)A2^(-3/2)A3 + 6m^(-3)A1^(-3/2)A2^(-1/2) + 3m^(-3)A1^(-3/2)A2^(1/2)A3^(-1) + 6m^(-3)A1^(-1/2)A2^(-3/2) + 16m^(-3)A1^(-1/2)A2^(-1/2)A3^(-1) + 5m^(-3)A1^(-1/2)A2^(1/2)A3^(-2) + 4m^(-3)A1^(1/2)A2^(-3/2)A3^(-1) + 7m^(-3)A1^(1/2)A2^(-1/2)A3^(-2) + m^(-2)A1^(-3/2)A2^(-3/2)A3^2 + 6m^(-2)A1^(-3/2)A2^(-1/2)A3 + 4m^(-2)A1^(-3/2)A2^(1/2) + 5m^(-2)A1^(-1/2)A2^(-3/2)A3 + 18m^(-2)A1^(-1/2)A2^(-1/2) + 13m^(-2)A1^(-1/2)A2^(1/2)A3^(-1) + m^(-2)A1^(-1/2)A2^(3/2)A3^(-2) + 4m^(-2)A1^(1/2)A2^(-3/2) + 15m^(-2)A1^(1/2)A2^(-1/2)A3^(-1) + 7m^(-2)A1^(1/2)A2^(1/2)A3^(-2) + 2m^(-2)A1^(3/2)A2^(-1/2)A3^(-2) + 3m^(-1)A1^(-3/2)A2^(-1/2)A3^2 + 4m^(-1)A1^(-3/2)A2^(1/2)A3 + 2m^(-1)A1^(-1/2)A2^(-3/2)A3^2 + 16m^(-1)A1^(-1/2)A2^(-1/2)A3 + 16m^(-1)A1^(-1/2)A2^(1/2) + 3m^(-1)A1^(-1/2)A2^(3/2)A3^(-1) + 3m^(-1)A1^(1/2)A2^(-3/2)A3 + 16m^(-1)A1^(1/2)A2^(-1/2) + 16m^(-1)A1^(1/2)A2^(1/2)A3^(-1) + 2m^(-1)A1^(1/2)A2^(3/2)A3^(-2) + 4m^(-1)A1^(3/2)A2^(-1/2)A3^(-1) + 3m^(-1)A1^(3/2)A2^(1/2)A3^(-2) + 2A1^(-3/2)A2^(1/2)A3^2 + 7A1^(-1/2)A2^(-1/2)A3^2 + 15A1^(-1/2)A2^(1/2)A3 + 4A1^(-1/2)A2^(3/2) + A1^(1/2)A2^(-3/2)A3^2 + 13A1^(1/2)A2^(-1/2)A3 + 18A1^(1/2)A2^(1/2) + 5A1^(1/2)A2^(3/2)A3^(-1) + 4A1^(3/2)A2^(-1/2) + 6A1^(3/2)A2^(1/2)A3^(-1) + A1^(3/2)A2^(3/2)A3^(-2) + 7mA1^(-1/2)A2^(1/2)A3^2 + 4mA1^(-1/2)A2^(3/2)A3 + 5mA1^(1/2)A2^(-1/2)A3^2 + 16mA1^(1/2)A2^(1/2)A3 + 6mA1^(1/2)A2^(3/2) + 3mA1^(3/2)A2^(-1/2)A3 + 6mA1^(3/2)A2^(1/2) + 2mA1^(3/2)A2^(3/2)A3^(-1) + 2m^2A1^(-1/2)A2^(3/2)A3^2 + 7m^2A1^(1/2)A2^(1/2)A3^2 + 6m^2A1^(1/2)A2^(3/2)A3 + m^2A1^(3/2)A2^(-1/2)A3^2 + 5m^2A1^(3/2)A2^(1/2)A3 + 2m^2A1^(3/2)A2^(3/2) + 3m^3A1^(1/2)A2^(3/2)A3^2 + 2m^3A1^(3/2)A2^(1/2)A3^2 + 2m^3A1^(3/2)A2^(3/2)A3 + m^4A1^(3/2)A2^(3/2)*A3^2

Vertex	Maslov	Rank
`(-3/2, -3/2, -2)`	-6	1
`(-3/2, -3/2, 2)`	-2	1
`(-3/2, 1/2, -2)`	-4	1
`(-3/2, 1/2, 2)`	0	2
`(-1/2, 3/2, -2)`	-2	1
`(-1/2, 3/2, 2)`	2	2
`(1/2, -3/2, -2)`	-4	2
`(1/2, -3/2, 2)`	0	1
`(3/2, -1/2, -2)`	-2	2
`(3/2, -1/2, 2)`	2	1
`(3/2, 3/2, -2)`	0	1
`(3/2, 3/2, 2)`	4	1

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Record

FL/HFL Links

`orderOption(int)`	`2768`
`namestring`	`L11a502{1;1}`
`statusstring`	`success`
`slugstring`	`L11a502_1_1_b362e881`
`result_filestring`	`details/L11a502_1_1_b362e881.json`
`complexity_scoreOption(int)`	`363`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`11`
`component_countOption(int)`	`3`
`girthOption(int)`	`6`
`total_rankOption(int)`	`400`
`wall_secondsOption(float)`	`0.003272`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`3`
`support_sizeOption(int)`	`70`
`vertex_countOption(int)`	`12`
`fibered_vertex_countOption(int)`	`8`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`28`
`alexander_vertex_countOption(int)`	`12`
`alexander_relationstring`	`not_computed`
`fk_countint`	`0`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L11a502_1_1_b362e881" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L11a502_1_1_b362e881`