name: combinatorial-enumeration description: Combinatorial object generation and counting allowed-tools:
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- 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
- Object Definition: Precisely define combinatorial objects
- Generation Strategy: Choose efficient generation methods
- Counting: Use generating functions for counting
- OEIS Lookup: Search for known sequences
Tools/Libraries
- OEIS
- SageMath combinat
- SymPy combinatorics