Integer partitions API

Counts the partitions p(n) of an integer into unordered positive summands, optionally bounded by max number of parts or max part size, via exact DP. Answers 'How many ways can 10 be written as a sum of positive integers?', 'p(n) with parts at most k?'.

Price$0.04per request

MethodPOST

Route/v1/gametheory/integer-partitions

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

combinatoricspartitionsnumber-theoryp-of-ncountingdynamic-programmingdiscretesummands

API URLhttps://x402.hexl.dev/v1/gametheory/integer-partitions

Integration docs

Example request

{
  "n": 10
}

Example response

{
  "n": 10,
  "partitions": 42,
  "partitionsExact": "42",
  "isExactInteger": true,
  "restriction": "none",
  "interpretation": "p(10) = 42: the number of ways to write 10 as an unordered sum of positive integers."
}

Input schema

{
  "type": "object",
  "required": [
    "n"
  ],
  "properties": {
    "n": {
      "type": "integer",
      "minimum": 0,
      "maximum": 400,
      "examples": [
        10
      ]
    },
    "maxParts": {
      "type": "integer",
      "minimum": 1
    },
    "maxPartSize": {
      "type": "integer",
      "minimum": 1,
      "examples": [
        3
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}