Babysitter combinatorics-calculator

claude-code science

Babysitter combinatorics-calculator

Calculate combinatorial values with modular arithmetic

install

source · Clone the upstream repo

git clone https://github.com/a5c-ai/babysitter

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/a5c-ai/babysitter "$T" && mkdir -p ~/.claude/skills && cp -r "$T/library/specializations/algorithms-optimization/skills/combinatorics-calculator" ~/.claude/skills/a5c-ai-babysitter-combinatorics-calculator && rm -rf "$T"

manifest: library/specializations/algorithms-optimization/skills/combinatorics-calculator/SKILL.md

tags

#combinatorics #modular-arithmetic #competitive-programming #number-theory #algorithm #math

source content

Combinatorics Calculator Skill

Purpose

Calculate combinatorial values with modular arithmetic support for competitive programming applications.

Capabilities

Factorial and inverse factorial precomputation
nCr, nPr with modular arithmetic
Catalan, Stirling, Bell numbers
Lucas theorem implementation
Inclusion-exclusion principle application
Generating functions

Target Processes

combinatorics-counting
number-theory-algorithms
dp-pattern-matching

Combinatorial Functions

Basic Counting

Factorial: n!
Permutations: P(n,r) = n!/(n-r)!
Combinations: C(n,r) = n!/(r!(n-r)!)

Special Numbers

Catalan numbers
Stirling numbers (first and second kind)
Bell numbers
Derangements

Advanced Techniques

Lucas theorem (for large n, small p)
Inclusion-exclusion
Burnside's lemma
Generating functions

Input Schema

{
  "type": "object",
  "properties": {
    "operation": {
      "type": "string",
      "enum": ["nCr", "nPr", "factorial", "catalan", "stirling", "lucas", "precompute"]
    },
    "n": { "type": "integer" },
    "r": { "type": "integer" },
    "mod": { "type": "integer" },
    "precomputeLimit": { "type": "integer" }
  },
  "required": ["operation"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "result": { "type": "integer" },
    "code": { "type": "string" },
    "formula": { "type": "string" }
  },
  "required": ["success"]
}