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integer marginal table family

Given1..3 labelled row totals and1..3 labelled column totals, each nonnegative integer vector with sum at most6, construct EVERY nonnegative integer matrix with exactly those margins. Return entire matrix family in ascending row-major lexicographic order, count, feasibility and both original totals. Row/column labels and zero-total rows/columns remain in their supplied order; do not quotient by permutations. Unequal grand totals are well-formed known-empty families. A zero grand total has.

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Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
row_sumsSiehe SchemaJa
column_sumsSiehe SchemaJa
claimed_tablesSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "type": "object",
  "additionalProperties": false,
  "required": [
    "row_sums",
    "column_sums",
    "claimed_tables"
  ],
  "properties": {
    "row_sums": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 3,
          "items": {
            "type": "integer",
            "minimum": 0,
            "maximum": 6
          },
          "minItems": 1
        },
        {
          "type": "null"
        }
      ]
    },
    "column_sums": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 3,
          "items": {
            "type": "integer",
            "minimum": 0,
            "maximum": 6
          },
          "minItems": 1
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_tables": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 32,
          "items": {
            "type": "array",
            "maxItems": 3,
            "items": {
              "type": "array",
              "maxItems": 3,
              "items": {
                "type": "integer",
                "minimum": 0,
                "maximum": 6
              }
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "row_sums": [
    1,
    1
  ],
  "column_sums": [
    1,
    1
  ],
  "claimed_tables": [
    [
      [
        0,
        1
      ],
      [
        1,
        0
      ]
    ],
    [
      [
        1,
        0
      ],
      [
        0,
        1
      ]
    ]
  ]
}

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

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