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noncrossing partial matching inventory

For 0 to 7 ordered points labelled from zero, enumerate all partial matchings: each point is paired at most once and arcs (i,j),(k,l) cannot have i<k<j<l. Nested pairs and unmatched singletons are allowed. Return every sorted pair list, singleton list, opening=1/closing=-1/singleton=0 stepword and all prefix heights including initial zero. Records sort lexicographically by stepword with -1<0<1. Return the whole pair-count histogram, including zero bins. Empty points have one empty matching..

POST https://datenvertrag.halowerk.com/v1/noncrossing-partial-matching-inventory

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
pointsSiehe SchemaJa
claimed_matchingsSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "$schema": "http://json-schema.org/draft-07/schema#",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "points",
    "claimed_matchings"
  ],
  "properties": {
    "points": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 0,
          "maximum": 7
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_matchings": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 127,
          "items": {
            "type": "array",
            "maxItems": 3,
            "items": {
              "type": "array",
              "minItems": 2,
              "maxItems": 2,
              "items": {
                "type": "integer",
                "minimum": 0,
                "maximum": 6
              }
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "points": 4,
  "claimed_matchings": [
    [],
    [
      [
        2,
        3
      ]
    ],
    [
      [
        1,
        2
      ]
    ],
    [
      [
        1,
        3
      ]
    ],
    [
      [
        0,
        1
      ]
    ],
    [
      [
        0,
        1
      ],
      [
        2,
        3
      ]
    ],
    [
      [
        0,
        2
      ]
    ],
    [
      [
        0,
        3
      ]
    ],
    [
      [
        0,
        3
      ],
      [
        1,
        2
      ]
    ]
  ]
}

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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

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