L11n371{0;1} - HFL and FL

details/L11n371_0_1_71b2de13.json

Multivariable Alexander polynomial

Δ_L
`-A1^(1/2)A2^(2) + A1^(1/2)A2^(2)A3^(-1) - A1^(1/2)A2A3 + 4A1^(1/2)A2 - 2A1^(1/2)A2A3^(-1) + 2A1^(1/2)A3 - 4A1^(1/2) + A1^(1/2)A3^(-1) - A1^(1/2)A2^(-1)A3 + A1^(1/2)A2^(-1) - A1^(-1/2)A2 + A1^(-1/2)A2A3^(-1) - A1^(-1/2)A3 + 4A1^(-1/2) - 2A1^(-1/2)A3^(-1) + 2A1^(-1/2)A2^(-1)A3 - 4A1^(-1/2)A2^(-1) + A1^(-1/2)A2^(-1)A3^(-1) - A1^(-1/2)A2^(-2)A3 + A1^(-1/2)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.

Interactive 3D view · hover a vertex for coordinates

Dual Thurston polytope

Vertex	Dual to fibered face
`(-1, -4, 2)`	yes
`(1, 4, -2)`	yes
`(1, -2, 2)`	yes
`(-1, 2, -2)`	yes
`(1, 0, -2)`	yes
`(-1, -2, -2)`	yes
`(1, 4, 0)`	yes
`(1, 2, 2)`	yes
`(-1, -4, 0)`	yes
`(-1, 2, 0)`	yes
`(1, -2, 0)`	yes
`(-1, 0, 2)`	yes

Interactive 3D view · hover a vertex for coordinates

HFL polytope

Poincaré polynomial
m^(-3)A1^(-1)A2^(-5/2)A3^(-1/2) + m^(-3)A1^(-1)A2^(-3/2)A3^(-3/2) + 2m^(-2)A1^(-1)A2^(-5/2)A3^(1/2) + 6m^(-2)A1^(-1)A2^(-3/2)A3^(-1/2) + 3m^(-2)A1^(-1)A2^(-1/2)A3^(-3/2) + m^(-2)A2^(-5/2)A3^(-1/2) + m^(-2)A2^(-3/2)A3^(-3/2) + m^(-1)A1^(-1)A2^(-5/2)A3^(3/2) + 8m^(-1)A1^(-1)A2^(-3/2)A3^(1/2) + 11m^(-1)A1^(-1)A2^(-1/2)A3^(-1/2) + 3m^(-1)A1^(-1)A2^(1/2)A3^(-3/2) + 2m^(-1)A2^(-5/2)A3^(1/2) + 7m^(-1)A2^(-3/2)A3^(-1/2) + 4m^(-1)A2^(-1/2)A3^(-3/2) + 3A1^(-1)A2^(-3/2)A3^(3/2) + 11A1^(-1)A2^(-1/2)A3^(1/2) + 8A1^(-1)A2^(1/2)A3^(-1/2) + A1^(-1)A2^(3/2)A3^(-3/2) + A2^(-5/2)A3^(3/2) + 10A2^(-3/2)A3^(1/2) + 17A2^(-1/2)A3^(-1/2) + 6A2^(1/2)A3^(-3/2) + A1A2^(-3/2)A3^(-1/2) + A1A2^(-1/2)A3^(-3/2) + 3mA1^(-1)A2^(-1/2)A3^(3/2) + 6mA1^(-1)A2^(1/2)A3^(1/2) + 2mA1^(-1)A2^(3/2)A3^(-1/2) + 4mA2^(-3/2)A3^(3/2) + 19mA2^(-1/2)A3^(1/2) + 19mA2^(1/2)A3^(-1/2) + 4mA2^(3/2)A3^(-3/2) + 2mA1A2^(-3/2)A3^(1/2) + 6mA1A2^(-1/2)A3^(-1/2) + 3mA1A2^(1/2)A3^(-3/2) + m^2A1^(-1)A2^(1/2)A3^(3/2) + m^2A1^(-1)A2^(3/2)A3^(1/2) + 6m^2A2^(-1/2)A3^(3/2) + 17m^2A2^(1/2)A3^(1/2) + 10m^2A2^(3/2)A3^(-1/2) + m^2A2^(5/2)A3^(-3/2) + m^2A1A2^(-3/2)A3^(3/2) + 8m^2A1A2^(-1/2)A3^(1/2) + 11m^2A1A2^(1/2)A3^(-1/2) + 3m^2A1A2^(3/2)A3^(-3/2) + 4m^3A2^(1/2)A3^(3/2) + 7m^3A2^(3/2)A3^(1/2) + 2m^3A2^(5/2)A3^(-1/2) + 3m^3A1A2^(-1/2)A3^(3/2) + 11m^3A1A2^(1/2)A3^(1/2) + 8m^3A1A2^(3/2)A3^(-1/2) + m^3A1A2^(5/2)A3^(-3/2) + m^4A2^(3/2)A3^(3/2) + m^4A2^(5/2)A3^(1/2) + 3m^4A1A2^(1/2)A3^(3/2) + 6m^4A1A2^(3/2)A3^(1/2) + 2m^4A1A2^(5/2)A3^(-1/2) + m^5A1A2^(3/2)A3^(3/2) + m^5A1A2^(5/2)A3^(1/2)

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

Interactive 3D view · hover a vertex for coordinates

Record

FL/HFL Links

`orderOption(int)`	`3346`
`namestring`	`L11n371{0;1}`
`statusstring`	`success`
`slugstring`	`L11n371_0_1_71b2de13`
`result_filestring`	`details/L11n371_0_1_71b2de13.json`
`complexity_scoreOption(int)`	`363`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`11`
`component_countOption(int)`	`3`
`girthOption(int)`	`6`
`total_rankOption(int)`	`288`
`wall_secondsOption(float)`	`0.003367`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`3`
`support_sizeOption(int)`	`58`
`vertex_countOption(int)`	`18`
`fibered_vertex_countOption(int)`	`12`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`20`
`alexander_vertex_countOption(int)`	`12`
`alexander_relationstring`	`not_computed`
`fk_countint`	`0`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L11n371_0_1_71b2de13" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L11n371_0_1_71b2de13`