Combinatorial object generation and counting
Scanned 9/2/2026
Install to Claude Code
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---
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
graph:
domains: [domain:mathematics]
specializations: [specialization:computational-mathematics]
skillAreas: [skill-area:mathematical-reasoning, skill-area:computational-geometry, skill-area:graph-algorithms]
workflows: [workflow:experiment-design]
roles: [role:computational-scientist, role:research-scientist]
---
# 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
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