HALOWERKDatenvertragswerk
latin square isotopy orbit stabilizer
For a complete Latin square L of order1..4 over labels0..n-1, return EVERY Latin square under independent row/column/symbol permutations and every stabilizing triple. Define action B[i][j]=symbols[L[rows[i]][columns[j]]]: rows and columns are newslot-to-originalslot maps, symbols maps old symbol to new symbol. Encode each B by sum B[i][j]*n^(i*n+j), first rowmajor entry leastsignificant. All distinct orbitcodes sorted numerically, minimumcode representative, orbit size, all autotopism.
POST https://datenvertrag.halowerk.com/v1/latin-square-isotopy-orbit-stabilizerEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| table | Siehe Schema | Ja | |
| claimed_artifact | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"additionalProperties": false,
"required": [
"table",
"claimed_artifact"
],
"properties": {
"table": {
"anyOf": [
{
"type": "array",
"maxItems": 4,
"items": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1
},
"minItems": 1
},
{
"type": "null"
}
]
},
"claimed_artifact": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"orbit_codes",
"canonical_code",
"orbit_size",
"autotopisms",
"stabilizer_order",
"group_order"
],
"properties": {
"orbit_codes": {
"type": "array",
"maxItems": 576,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 4294967295
}
},
"canonical_code": {
"type": "integer",
"minimum": 0,
"maximum": 4294967295
},
"orbit_size": {
"type": "integer",
"minimum": 0,
"maximum": 13824
},
"autotopisms": {
"type": "array",
"maxItems": 128,
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"rows",
"columns",
"symbols"
],
"properties": {
"rows": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1
},
"columns": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1
},
"symbols": {
"type": "array",
"maxItems": 4,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1
}
}
}
},
"stabilizer_order": {
"type": "integer",
"minimum": 0,
"maximum": 13824
},
"group_order": {
"type": "integer",
"minimum": 0,
"maximum": 13824
}
}
},
{
"type": "null"
}
]
}
}
}Veröffentlichtes Eingabebeispiel
{
"table": [
[
0,
1
],
[
1,
0
]
],
"claimed_artifact": {
"orbit_codes": [
6,
9
],
"canonical_code": 6,
"orbit_size": 0,
"autotopisms": [
{
"rows": [
0,
1
],
"columns": [
0,
1
],
"symbols": [
0,
1
]
},
{
"rows": [
0,
1
],
"columns": [
1,
0
],
"symbols": [
1,
0
]
},
{
"rows": [
1,
0
],
"columns": [
0,
1
],
"symbols": [
1,
0
]
},
{
"rows": [
1,
0
],
"columns": [
1,
0
],
"symbols": [
0,
1
]
}
],
"stabilizer_order": 4,
"group_order": 8
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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