{
  "context": "This criteria evaluates how well the engineer uses mathjs's advanced combinatorics functions (stirlingS2, bellNumbers, catalan) to solve partition and sequence counting problems. The assessment focuses exclusively on proper usage of these specialized mathjs functions.",
  "type": "weighted_checklist",
  "checklist": [
    {
      "name": "Uses stirlingS2 function",
      "description": "The countSetPartitions function uses mathjs's stirlingS2(n, k) function to compute the number of ways to partition n elements into k non-empty subsets (Stirling numbers of the second kind).",
      "max_score": 30
    },
    {
      "name": "Uses bellNumbers function",
      "description": "The countTotalPartitions function uses mathjs's bellNumbers(n) function to compute the total number of ways to partition n elements.",
      "max_score": 30
    },
    {
      "name": "Uses catalan function",
      "description": "The countBinaryTrees function uses mathjs's catalan(n) function to compute the number of distinct binary tree structures with n nodes.",
      "max_score": 30
    },
    {
      "name": "Proper error handling",
      "description": "All three functions properly validate inputs (checking for negative values and invalid k > n cases) before calling mathjs functions, throwing appropriate errors as specified in the API.",
      "max_score": 10
    }
  ]
}