---
name: combinatorial-enumeration
description: Combinatorial object generation and counting
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - Grep
metadata:
  specialization: mathematics
  domain: science
  category: combinatorics
  phase: 6
---

# Combinatorial Enumeration

## Purpose

Provides combinatorial object generation and counting capabilities for discrete mathematics.

## Capabilities

- Permutation and combination generation
- Partition enumeration
- Generating function computation
- OEIS sequence lookup
- Polya enumeration
- Species theory computations

## Usage Guidelines

1. **Object Definition**: Precisely define combinatorial objects
2. **Generation Strategy**: Choose efficient generation methods
3. **Counting**: Use generating functions for counting
4. **OEIS Lookup**: Search for known sequences

## Tools/Libraries

- OEIS
- SageMath combinat
- SymPy combinatorics