HALOWERKDatenvertragswerk
simultaneous core partition family
For supplied coprime positive integers a,b each1..5, synthesize EVERY simultaneous(a,b)-core integer partition: no cell hook length is divisible by either parameter. No original partition is supplied. Return all nonincreasing positive rowlength arrays in numeric lexicographic order, each entire rowaligned hook tableau, each descending firstcolumn-hook beta-set, the size histogram indexed0..15, and exact family count. Include the empty partition and empty tableaux/beta-set. a=1 or b=1 gives.
POST https://datenvertrag.halowerk.com/v1/simultaneous-core-partition-familyEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| a | Siehe Schema | Ja | |
| b | Siehe Schema | Ja | |
| claim | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"$schema": "http://json-schema.org/draft-07/schema#",
"type": "object",
"additionalProperties": false,
"required": [
"a",
"b",
"claim"
],
"properties": {
"a": {
"anyOf": [
{
"type": "integer",
"minimum": 1,
"maximum": 5
},
{
"type": "null"
}
]
},
"b": {
"anyOf": [
{
"type": "integer",
"minimum": 1,
"maximum": 5
},
{
"type": "null"
}
]
},
"claim": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"partitions",
"hook_tableaux",
"beta_sets",
"size_histogram",
"count"
],
"properties": {
"partitions": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 1,
"maximum": 15
},
"minItems": 0,
"maxItems": 15
},
"minItems": 0,
"maxItems": 14
},
"hook_tableaux": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 1,
"maximum": 15
},
"minItems": 1,
"maxItems": 15
},
"minItems": 0,
"maxItems": 15
},
"minItems": 0,
"maxItems": 14
},
"beta_sets": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 1,
"maximum": 15
},
"minItems": 0,
"maxItems": 15
},
"minItems": 0,
"maxItems": 14
},
"size_histogram": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 14
},
"minItems": 16,
"maxItems": 16
},
"count": {
"type": "integer",
"minimum": 0,
"maximum": 14
}
}
},
{
"type": "null"
}
]
}
}
}Veröffentlichtes Eingabebeispiel
{
"a": 1,
"b": 1,
"claim": {
"partitions": [
[]
],
"hook_tableaux": [
[]
],
"beta_sets": [
[]
],
"size_histogram": [
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"count": 1
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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